Lakshmikantham Nonlinear Phenomena in Mathematical Sciences

Proceedings of an International Conference on Nonlinear Phenomena in Mathematical Sciences, Held at the University of Texas at Arlington, Arlington, Texas, June 16-20, 1980
1. Auflage 2014
ISBN: 978-1-4832-7205-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 1062 Seiten, Web PDF

Nonlinear Phenomena in Mathematical Sciences contains the proceedings of an International Conference on Nonlinear Phenomena in Mathematical Sciences, held at the University of Texas at Arlington, on June 16-20,1980. The papers explore trends in nonlinear phenomena in mathematical sciences, with emphasis on nonlinear functional analytic methods and their applications; nonlinear wave theory; and applications to medical and life sciences. In the area of nonlinear functional analytic methods and their applications, the following subjects are discussed: optimal control theory; periodic oscillations of nonlinear mechanical systems; Leray-Schauder degree theory; differential inequalities applied to parabolic and elliptic partial differential equations; bifurcation theory, stability theory in analytical mechanics; singular and ordinary boundary value problems, etc. The following topics in nonlinear wave theory are considered: nonlinear wave propagation in a randomly homogeneous media; periodic solutions of a semilinear wave equation; asymptotic behavior of solutions of strongly damped nonlinear wave equations; shock waves and dissipation theoretical methods for a nonlinear Schr?dinger equation; and nonlinear hyperbolic Volterra equations occurring in viscoelasticity. Applications to medical and life sciences include mathematical modeling in physiology, pharmacokinetics, and neuro-mathematics, along with epidemic modeling and parameter estimation techniques. This book will be helpful to students, practitioners, and researchers in the field of mathematics.

Autoren/Hrsg.

Lakshmikantham, V.

Inhaltsverzeichnis

1;Front Cover;1
2;Nonlinear Phenomena in Mathematical Sciences;4
3;Copyright Page;5
4;Table of Contents;6
5;CONTRIBUTORS;14
6;PREFACE;22
7;HONORING PROFESSOR LAMBERTO CESARI;24
8;PART I: INVITED ADDRESSES AND RESEARCH REPORTS;28
8.1;CHAPTER 1. GROUP PROPERTIES
OF;28
8.1.1;I. INTRODUCTION;28
8.1.2;II. PHYSICAL EXAMPLES;28
8.1.3;III. CANONICAL EQUATION;29
8.1.4;IV. FULL GROUP FOR (1);30
8.1.5;V. APPLICATIONS;32
8.1.6;REFERENCES;32
8.2;CHAPTER 2. PERTURBATION AND BIFURCATION IN A DISCONTINUOUS NONLINEAR EIGENVALUE PROBLEM;34
8.2.1;I. INTRODUCTION;34
8.2.2;II. THE REDUCED PROBLEM;34
8.2.3;III. PERTURBATION OF THE REDUCED PROBLEM;35
8.2.4;IV. AN INTEGRAL EQUATION FOR THE FREE BOUNDARY;36
8.2.5;V. SOLUTION OF THE NONLINEAR INTEGRAL EQUATION;37
8.2.6;REFERENCES;38
8.3;CHAPTER 3. A SINGULAR FOURIER PROBLEM WITH NONLINEAR BOUNDARY CONDITION;40
8.3.1;REFERENCES;41
8.4;CHAPTER 4. DIVERSITY AND SPATIAL EFFECTS ON COMPETITIVE SYSTEMS;42
8.4.1;I. INTRODUCTION;42
8.4.2;II. A SPATIALLY HOMOGENEOUS COMPETITION MODEL;42
8.4.3;III. A THREE DIMENSIONAL MODEL OF COMPETITION;43
8.4.4;IV. A DISCRETE SPATIALLY HETEROGENEOUS COMPETITION MODEL;46
8.4.5;V. A CONTINUOUSLY DISTRIBUTED COMPETITIVE MODEL;48
8.4.6;VI. SUMMARY;50
8.4.7;REFERENCES;50
8.5;CHAPTER 5. A BANG-BANG TYPE THEOREM FOR MEASURES;52
8.5.1;I. INTRODUCTION;52
8.5.2;II. RESULTS;53
8.5.3;REFERENCES;57
8.6;CHAPTER 6. SOME OPTIMAL CONTROL PROBLEMS FOR THE HELMHOLTZ EQUATION;58
8.6.1;I. INTRODUCTION;58
8.6.2;II. FORMULATION OF THE LINEAR PROBLEM;59
8.6.3;III. THE NONLINEAR PROBLEM;61
8.6.4;REFERENCES;65
8.7;CHAPTER 7. STABILITY OF A LARGE FLEXIBLE BEAM IN SPACE;66
8.7.1;A SHORT NOTE;66
8.8;CHAPTER 8. SOME CONSTRUCTIONS IN SEMI-DYNAMICAL SYSTEMS;68
8.8.1;I. INTRODUCTION;68
8.8.2;II. PRELIMINARIES;68
8.8.3;III. START POINTS;69
8.8.4;IV. DIRECT SUMS OF SEMI-DYNAMICAL SYSTEMS;69
8.8.5;V. SUB-SEMI-DYNAMICAL SYSTEMS;70
8.8.6;VI. PRODUCTS OF SEMI-DYNAMICAL SYSTEMS;72
8.8.7;REFERENCES;72
8.9;CHAPTER 9. IDENTIFICATION OF NONLINEAR DELAY SYSTEMS USING SPLINE METHODS;74
8.9.1;I. INTRODUCTION;74
8.9.2;II. STATE APPROXIMATION FOR NONLINEAR SYSTEMS;75
8.9.3;III. PARAMETER IDENTIFICATION PROBLEMS;79
8.9.4;REFERENCES;82
8.10;CHAPTER 10. PARAMETER ESTIMATION TECHNIQUES FOR NONLINEAR DISTRIBUTED PARAMETER SYSTEMS;84
8.10.1;I. INTRODUCTION;84
8.10.2;II. THE IDENTIFICATION PROBLEM;84
8.10.3;III. MODAL APPROXIMATIONS: CONVERGENCE RESULTS;87
8.10.4;IV.
APPROXIMATION OF THE IDENTIFICATION PROBLEM;92
8.10.5;V. NUMERICAL RESULTS;93
8.10.6;REFERENCES;94
8.11;CHAPTER 11. PROJECTION TECHNIQUES FOR NONLINEAR ELLIPTIC PDE;96
8.11.1;I. INTRODUCTION;96
8.11.2;II. MONOTONE PERTURBATIONS OF THE LAPLACIAN;98
8.11.3;III. PERTURBATIONS OF ORDER ZERO;100
8.11.4;IV. A RESULT OF EXISTENCE IN DENSITY;102
8.11.5;REFERENCES;103
8.12;CHAPTER 12. AN OPERATIONAL EQUATION ARISING IN SYNTHESIS OF OPTIMAL CONTROL;106
8.12.1;I. SYNTHESIS OF OPTIMAL CONTROL;106
8.12.2;II. SOLUTION TO EQUATION 1.10;107
8.12.3;REFERENCES;113
8.13;CHAPTER 13. THE PROBLEM OF GRAFFI-CESARI;114
8.13.1;I. THE PHYSICAL AND MATHEMATICAL PROBLEM;114
8.13.2;II.
CESARI'S EXISTENCE THEOREM;115
8.13.3;III. A METHOD OF SUCCESSIVE APPROXIMATIONS;119
8.13.4;IV. FURTHER DEVELOPMENTS;119
8.13.5;V. THE NONLINEAR BV PROBLEM AS THE LIMIT OF LINEAR BV PROBLEMS;120
8.13.6;VI. A COMPARISON WITH THE PERTURBATIVE METHOD FOR THE LASER PROBLEM;124
8.13.7;VII. AN ABSTRACT ITERATIVE METHOD;125
8.13.8;REFERENCES;127
8.14;CHAPTER 14. A VARIATIONAL APPROACH TO SOLVING SEMILINEAR EQUATIONS AT RESONANCE;130
8.14.1;I. INTRODUCTION;130
8.14.2;II. ABSTRACT RESULTS;130
8.14.3;III. APPLICATIONS;136
8.14.4;REFERENCES;139
8.15;CHAPTER 15. EXCHANGE OF STABILITY AND HOPF BIFURCATION;140
8.15.1;I. INTRODUCTION;28
8.15.2;II. PHYSICAL EXAMPLES;28
8.15.3;III.
CANONICAL EQUATION;29
8.15.4;IV. FULL GROUP FOR (1);30
8.15.5;V. APPLICATIONS;32
8.15.6;REFERENCES;32
8.16;CHAPTER 16. PERTURBATION AND BIFURCATION IN A DISCONTINUOUS NONLINEAR EIGENVALUE PROBLEM;34
8.16.1;I. INTRODUCTION;34
8.16.2;II. THE REDUCED PROBLEM;34
8.16.3;III. PERTURBATION OF THE REDUCED PROBLEM;35
8.16.4;IV. AN INTEGRAL EQUATION FOR THE FREE BOUNDARY;36
8.16.5;V. SOLUTION OF THE NONLINEAR INTEGRAL EQUATION;37
8.16.6;REFERENCES;38
8.17;CHAPTER 17. A SINGULAR FOURIER PROBLEM WITH NONLINEAR BOUNDARY CONDITION;40
8.17.1;REFERENCES;41
8.18;CHAPTER 18. DIVERSITY AND SPATIAL EFFECTS ON COMPETITIVE SYSTEMS;42
8.18.1;I. INTRODUCTION;42
8.18.2;II. A SPATIALLY HOMOGENEOUS COMPETITION MODEL;42
8.18.3;III. A THREE DIMENSIONAL MODEL OF COMPETITION;43
8.18.4;IV. A DISCRETE SPATIALLY HETEROGENEOUS COMPETITION MODEL;46
8.18.5;V. A CONTINUOUSLY DISTRIBUTED COMPETITIVE MODEL;48
8.18.6;VI. SUMMARY;50
8.18.7;REFERENCES;50
8.19;CHAPTER 19. A BANG-BANG TYPE THEOREM FOR MEASURES;52
8.19.1;I. INTRODUCTION;52
8.19.2;II. RESULTS;53
8.19.3;REFERENCES;57
8.20;CHAPTER 20. SOME OPTIMAL CONTROL PROBLEMS FOR THE HELMHOLTZ EQUATION;58
8.20.1;I. INTRODUCTION;58
8.20.2;II. FORMULATION OF THE LINEAR PROBLEM;59
8.20.3;III. THE NONLINEAR PROBLEM;61
8.20.4;REFERENCES;65
8.21;CHAPTER 21. STABILITY OF A LARGE FLEXIBLE BEAM IN SPACE;66
8.21.1;A SHORT NOTE;66
8.22;CHAPTER 22. SOME CONSTRUCTIONS IN SEMI-DYNAMICAL SYSTEMS;68
8.22.1;I. INTRODUCTION;68
8.22.2;II. PRELIMINARIES;68
8.22.3;III. START POINTS;69
8.22.4;IV. DIRECT SUMS OF SEMI-DYNAMICAL SYSTEMS;69
8.22.5;V. SUB-SEMI-DYNAMICAL SYSTEMS;70
8.22.6;VI. PRODUCTS OF SEMI-DYNAMICAL SYSTEMS;72
8.22.7;REFERENCES;72
8.23;CHAPTER 23. IDENTIFICATION OF NONLINEAR DELAY SYSTEMS USING SPLINE METHODS;74
8.23.1;I. INTRODUCTION;74
8.23.2;II. STATE APPROXIMATION FOR NONLINEAR SYSTEMS;75
8.23.3;III. PARAMETER IDENTIFICATION PROBLEMS;79
8.23.4;REFERENCES;82
8.24;CHAPTER 24. PARAMETER ESTIMATION TECHNIQUES FOR NONLINEAR DISTRIBUTED PARAMETER SYSTEMS;84
8.24.1;I. INTRODUCTION;84
8.24.2;II. THE IDENTIFICATION PROBLEM;84
8.24.3;III. MODAL APPROXIMATIONS: CONVERGENCE RESULTS;87
8.24.4;IV .
APPROXIMATION OF THE IDENTIFICATION PROBLEM;92
8.24.5;V. NUMERICAL RESULTS;93
8.24.6;REFERENCES;94
8.25;CHAPTER 25. PROJECTION TECHNIQUES FOR NONLINEAR ELLIPTIC PDE;96
8.25.1;I. INTRODUCTION;96
8.25.2;II. MONOTONE PERTURBATIONS OF THE LAPLACIAN;98
8.25.3;III. PERTURBATIONS OF ORDER ZERO;100
8.25.4;IV. A RESULT OF EXISTENCE IN DENSITY;102
8.25.5;REFERENCES;103
8.26;CHAPTER 26. AN OPERATIONAL EQUATION ARISING IN SYNTHESIS OF OPTIMAL CONTROL;106
8.26.1;I. SYNTHESIS OF OPTIMAL CONTROL;106
8.26.2;II. SOLUTION TO EQUATION 1.10;107
8.26.3;REFERENCES;113
8.27;CHAPTER 27. THE PROBLEM OF GRAFFI-CESARI;114
8.27.1;I. THE PHYSICAL AND MATHEMATICAL PROBLEM;114
8.27.2;II.
CESARI'S EXISTENCE THEOREM;115
8.27.3;III. A METHOD OF SUCCESSIVE APPROXIMATIONS;119
8.27.4;IV. FURTHER DEVELOPMENTS;119
8.27.5;V. THE NONLINEAR BV PROBLEM AS THE LIMIT OF LINEAR BV PROBLEMS;120
8.27.6;VI. A COMPARISON WITH THE PERTURBATIVE METHOD FOR THE LASER PROBLEM;124
8.27.7;VII. AN ABSTRACT ITERATIVE METHOD;125
8.27.8;REFERENCES;127
8.28;CHAPTER 28. A VARIATIONAL APPROACH TO SOLVING SEMILINEAR EQUATIONS AT RESONANCE;130
8.28.1;I. INTRODUCTION;130
8.28.2;II. ABSTRACT RESULTS;130
8.28.3;III. APPLICATIONS;136
8.28.4;REFERENCES;139
8.29;CHAPTER 29. EXCHANGE OF STABILITY AND HOPF BIFURCATION;140
8.29.1;I. INTRODUCTION;140
8.29.2;II. GENERALIZED TRANSVERSALITY CONDITION;141
8.29.3;III. CHANGE OF STABILITY;142
8.29.4;REFERENCES;143
8.30;CHAPTER 30. MONOTONE METHOD FOR NONLINEAR BOUNDARY VALUE PROBLEMS BY LINEARIZATION TECHNIQUES;144
8.30.1;I. INTRODUCTION;144
8.30.2;II. NOTATION AND HYPOTHESES;145
8.30.3;III. PRELIMINARY LEMMAS;147
8.30.4;IV. MONOTONE METHOD;148
8.30.5;REFERENCES;149
8.31;CHAPTER 31. EXISTENCE AND UNIQUENESS OF SOLUTIONS TO NONLINEAR-OPERATOR-DIFFERENTIAL EQUATIONS GENERALIZING DYNAMICAL SYSTEMS OF AUTOMATIC SPACESHIP NAVIGATION;150
8.31.1;I. INTRODUCTION;150
8.31.2;II. TIME DELAY OPERATOR;152
8.31.3;III. OPERATORS ASSOCIATED WITH AUTOMATIC CONTROL OF SPACESHIPS;153
8.31.4;IV.
OPERATORS OF EXPONENTIAL TYPE;155
8.31.5;V. LIPSCHITZIAN FUNCTIONS INDUCE OPERATORS OF EXPONENTIAL TYPE;158
8.31.6;VI. PROPERTIES OF A VOLTERRA INTEGRAL OPEATOR;159
8.31.7;VII. DYNAMICAL SYSTEMS WITH AUTOMATIC CONTROLS OF EXPONENTIAL TYPE;160
8.31.8;VIII. APPLICATION TO AN AUTOMATIC CONTROL OF SPACESHIPS;161
8.31.9;IX. CONCLUSIONS;162
8.31.10;REFERENCES;163
8.32;CHAPTER 32. A NUMERICAL METHOD FOR A FREE SURFACE DENSITY-DRIVEN FLOW;164
8.32.1;I. INTRODUCTION;164
8.32.2;II. THE EQUATIONS OF MOTION;165
8.32.3;III. PRESSURE EVALUATION;167
8.32.4;IV. THE TRANSPORT EQUATION;168
8.32.5;V. FREE SURFACE MOVEMENT;169
8.32.6;VI. SUMMARY OF A CALCULATIONAL STEP;170
8.32.7;VII. STABILITY CONSIDERATION;170
8.32.8;VIII. COMPUTATIONAL EXAMPLE;170
8.32.9;REFERENCES;172
8.33;CHAPTER 33. VORTEX MOTIONS AND THEIR STABILITY;174
8.33.1;I. INTRODUCTION;174
8.33.2;II. EVOLUTION OF VORTEX;174
8.33.3;Ill.
UNIVALENT FUNCTIONS;176
8.33.4;IV. CONFORMAL
REPRESENTATION OF VORTEX;177
8.33.5;V. VARIATION OF THE VORTEX;178
8.33.6;VI. APPLICATIONS;181
8.33.7;REFERENCES;185
8.34;CHAPTER 34. THE HAMILTON-JACOBI EQUATION WITH AN UNBOUNDED INHOMOGENEITY;186
8.34.1;I. INTRODUCTION;186
8.34.2;II. THE HOMOGENEOUS CASE;188
8.34.3;III. THE MAIN RESULT;189
8.34.4;VI.
REMARKS;191
8.34.5;V.
A RELATED PROBLEM;192
8.34.6;REFERENCES;193
8.35;CHAPTER 35. FINITE DIFFERENCE METHODS FOR IDENTIFICATION OF HEREDITARY CONTROL SYSTEMS;196
8.35.1;I . INTRODUCTION;196
8.35.2;II.
PROBLEM FORMULATION;196
8.35.3;III.
THE EULER APPROXIMATION;198
8.35.4;IV. NONLINEAR SYSTEMS AND HIGHER ORDER METHODS;200
8.35.5;V. NUMERICAL EXAMPLES;201
8.35.6;REFERENCES;205
8.36;CHAPTER 36. MODELS OF VERTICALLY TRANSMITTED DISEASES WITH SEQUENTIAL-CONTINUOUS DYNAMICS;206
8.36.1;I. INTRODUCTION;206
8.36.2;II. THE MATHEMATICAL MODEL AND RESULTS;208
8.36.3;III. MODELS WITH SEQUENTIAL-CONTINUOUS DYNAMICS;213
8.36.4;ACKNOWLEDGMENTS;213
8.36.5;REFERENCES;214
8.37;CHAPTER 37. VERTICALLY TRANSMITTED DISEASES;216
8.37.1;I. INHERITANCE OF INFECTION;216
8.37.2;II. CLASSIFICATION OF MODELS;217
8.37.3;III. AN EXAMPLE: KEYSTONE VIRUS;218
8.37.4;IV. A MODEL WITH AGE-DEPENDENCE;220
8.37.5;REFERENCES;224
8.38;CHAPTER 38. A STOCHASTIC COMPARTMENTAL MODEL OF PREINFARCTION ANGINA;226
8.38.1;I. INTRODUCTION;226
8.38.2;II. THE DIGRAPH MODEL;226
8.38.3;III. DATA;227
8.38.4;IV. PARAMETER ESTIMATION;228
8.38.5;V. DISCUSSION AND CONCLUSIONS;232
8.38.6;ACKNOWLEDGMENTS;232
8.38.7;REFERENCES;232
8.38.8;APPENDIX 1;233
8.39;CHAPTER 39. A NONLINEAR DIFFUSION
SYSTEM MODELLING THE SPREAD OF ORO-FAECAL DISEASES;234
8.39.1;I. INTRODUCTION;234
8.39.2;II. THE PROBLEM;235
8.39.3;III. QUALITATIVE RESULTS FOR THE SPATIALLY HOMOGENEOUS CASE;236
8.39.4;IV. POSITIVITY OF THE SOLUTION;237
8.39.5;V. QUALITATIVE ANALYSIS OF THE VECTOR
FIELD;238
8.39.6;VI. ASYMPTOTIC BEHAVIOUR OF THE SOLUTIONS;241
8.39.7;VII. CONCLUSIONS;243
8.39.8;ACKNOWLEDGMENTS;244
8.39.9;REFERENCES;244
8.39.10;ADDENDUM;244
8.40;CHAPTER 40. EXISTENCE OF SOLUTIONS OF HYPERBOLIC PROBLEMS;246
8.40.1;I. THE CANONIC DECOMPOSITION AND THE ALTERNATIVE PROBLEM;246
8.40.2;II. THE CASE OF X0
LARGE WITH RESPECT TO ker E;248
8.40.3;III. THE CASE FOR
X0 = ker E;250
8.40.4;IV. LIENARD SYSTEMS;251
8.40.5;V. THE WORK OF LANDESMAN, LAZER, AND WILLIAMS;252
8.40.6;VI. SHAW'S EXTENSION OF LANDESMAN-LAZER THEOREM;253
8.40.7;VII. A GENERIC CHARACTERIZATION OF THE SET OF SOLUTIONS IN LANDESMAN-LAZER TYPE THEOREMS;254
8.40.8;VIII. THE ABSTRACT EXISTENCE THEOREM;255
8.40.9;IX.
THE HYPERBOLIC PROBLEM;256
8.40.10;X. SOME RESULTS ON QUASILINEAR HYPERBOLIC SYSTEMS;258
8.40.11;REFERENCES;259
8.41;CHAPTER 41. APPLICATIONS OF DIFFERENTIAL INEQUALITIES TO GAS LUBRICATION THEORY;262
8.41.1;I. INTRODUCTION;262
8.41.2;II. ANALYSIS;263
8.41.3;III. CONCLUSIONS;264
8.41.4;REFERENCES;266
8.42;CHAPTER 42. COMPARISON PRINCIPLE AND THEORY OF NONLINEAR BOUNDARY VALUE PROBLEMS;268
8.42.1;I. COMPARISON PRINCIPLE;268
8.42.2;II. EXISTENCE;270
8.42.3;III. UNIQUENESS AND STABILITY;271
8.42.4;IV. EXISTENCE OF PERIODIC SOLUTIONS;273
8.42.5;REFERENCES;274
8.43;CHAPTER 43. DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS NONLINEARITIES;276
8.43.1;REFERENCES;280
8.44;CHAPTER 44. AN ESTIMATE FOR THE SOLUTION OF A CERTAIN FUNCTIONAL DIFFERENTIAL EQUATION OF NEUTRAL TYPE;282
8.44.1;I. INTRODUCTION;282
8.44.2;II. NOTATIONS, DEFINITIONS AND PRELIMINARIES;282
8.44.3;III. MAIN RESULTS;286
8.44.4;REFERENCES;294
8.45;CHAPTER 45. A SEMIDISCRETIZATION PROCEDURE FOR FITZHUGH-NAGUMO EQUATIONS;296
8.45.1;I. INTRODUCTION;296
8.45.2;II. THE ODE APPROXIMATING SYSTEM;297
8.45.3;III. THE THRESHOLD PROBLEM FOR THE SYSTEM (12);300
8.45.4;IV. ANOTHER CASE FOR THE THRESHOLD PROBLEM;302
8.45.5;V. THE GENERAL CASE FOR f
(v);303
8.45.6;VI. SOME OPEN PROBLEMS;304
8.45.7;REFERENCES;305
8.46;CHAPTER 46. BIFURCATION OF PERIODIC SOLUTIONS OF NONLINEAR EQUATIONS IN AGE-STRUCTURED POPULATION DYNAMICS;306
8.46.1;I. INTRODUCTION;306
8.46.2;II. LINEAR EQUATIONS;308
8.46.3;III.
A BIFURCATION THEOREM;310
8.46.4;IV. A HOPF-TYPE BIFURCATION THEOREM;311
8.46.5;V. AN APPLICATION;313
8.46.6;REFERENCES;315
8.47;CHAPTER 47. CONSERVATION LAWS WITH DISSIPATION;316
8.47.1;I. INTRODUCTION;316
8.47.2;II. COMPLETE PARABOLIC DAMPING;317
8.47.3;III. INCOMPLETE PARABOLIC DAMPING;317
8.47.4;IV. VISCOUS DAMPING INDUCED BY MEMORY EFFECTS;319
8.47.5;REFERENCES;321
8.48;CHAPTER 48. ON FIXED POINTS OF MULTIVALUED MAPS;322
8.48.1;I. INTRODUCTION;322
8.48.2;II. PRELIMINARIES;322
8.48.3;III.;323
8.48.4;REFERENCES;327
8.49;CHAPTER 49. BIFURCATION OF STABLE PERIODIC SOLUTIONS FOR
PERIODIC QUASILINEAR PARABOLIC EQUATIONS;328
8.49.1;I. INTRODUCTION;328
8.49.2;II. THE CASE e <_
0;329
8.49.3;III. THE CASE e >0 : I;330
8.49.4;IV. THE CASE e > 0: II;331
8.49.5;REFERENCES;333
8.50;CHAPTER 50. CONTINUITY OF WEAK SOLUTIONS TO CERTAIN SINGULAR PARABOLIC EQUATIONS;334
8.50.1;I. THE RESULTS;334
8.50.2;II. THE MAIN PROPOSITION;336
8.50.3;III. CONTINUITY UP TO THE BOUNDARY;337
8.50.4;REFERENCES;339
8.51;CHAPTER 51. A PROBLEM ARISING IN THE MATHEMATICAL THEORY OF EPIDEMICS;340
8.51.1;I. INTRODUCTION;340
8.51.2;II. PRELIMINARIES;341
8.51.3;III.
EXISTENCE AND UNIQUENESS RESULTS;343
8.51.4;IV. REGULARITY RESULTS;349
8.51.5;V. AN EXAMPLE;351
8.51.6;REFERENCES;354
8.52;CHAPTER 52. A COLLINEAR tt-BODY PROBLEM OF CLASSICAL
ELECTRODYNAMICS;356
8.52.1;REFERENCES;361
8.53;CHAPTER 53. ON QUALITATIVE PROPERTIES OF NONLINEAR COMPARTMENTAL SYSTEMS;362
8.53.1;I. INTRODUCTION;362
8.53.2;II. REACHABILITY AND POSITIVITY;364
8.53.3;III. WASHOUT;366
8.53.4;REFERENCES;368
8.54;CHAPTER 54. THE ASYMPTOTIC FORM OF NONOSCILLATORY SOLUTIONS TO FOURTH ORDER EQUATIONS;370
8.54.1;I. INTRODUCTION;370
8.54.2;II. NONOSCILLATORY SOLUTIONS;370
8.54.3;III. THE ASYMPTOTIC FORM;372
8.54.4;REFERENCES;377
8.55;CHAPTER 55. IDENTIFICATION OF NONLINEAR COMPARTMENTAL SYSTEMS WITH AN APPLICATION TO THE MODELLING OF THE ENZYME CYTOCHROME P-450;378
8.55.1;I. INTRODUCTION;378
8.55.2;II. STUDY OF NONLINEARITY;380
8.55.3;III. IDENTIFICATION OF THE MODEL PARAMETERS;384
8.55.4;IV. DISCUSSION;387
8.55.5;REFERENCES;389
8.56;CHAPTER 56. SOME APPLICATIONS OF HADAMARD'S INVERSE FUNCTION THEOREM;390
8.56.1;I. FOURTH ORDER EQUATIONS;390
8.56.2;II. PARABOLIC SYSTEMS;392
8.56.3;REFERENCES;395
8.57;CHAPTER 57. COMPARISON THEOREMS FOR RICCATI DIFFERENTIAL EQUATIONS IN A
B-ALGEBRA;398
8.57.1;I. INTRODUCTION;398
8.57.2;II. SOME EXAMPLES;399
8.57.3;III. PROOF OF THEOREM
2.1;400
8.57.4;REFERENCES;404
8.58;CHAPTER 58. OSCILLATIONS PERIODIQUES DES SYSTEMES MECANIQUES NON LINEAIRES EXCITEES PAR DES DISTRIBUTIONS d (PERCUSSIONS) OU
d;406
8.58.1;I. EXCITATIONS ENGENDRANT DES SOLUTIONS CONTINUES;406
8.58.2;II.
SYSTEME NON LINEAIRE A EXCITATIONS PERIODIQUE PAR DES PERCUSSIONS S ET LEURS DERIVEES d ';410
8.58.3;REFERENCES;414
8.59;CHAPTER 59. REPRESENTATION AND ASYMPTOTIC BEHAVIOR OF STRONGLY DAMPED EVOLUTION EQUATIONS;416
8.59.1;I. INTRODUCTION;416
8.59.2;REFERENCES;423
8.60;CHAPTER 60. DEGREE THEORETIC METHODS IN OPTIMAL CONTROL;424
8.60.1;I. INTRODUCTION;424
8.60.2;II. A COINCIDENCE DEGREE FOR (L,N);425
8.60.3;III. THE EXISTENCE THEOREM;425
8.60.4;REFERENCES;426
8.61;CHAPTER 61. A GALERKIN NUMERICAL METHOD FOR A CLASS OF NONLINEAR REACTION-DIFFUSION SYSTEMS;428
8.61.1;I. INTRODUCTION;428
8.61.2;II. PRELIMINARIES AND GALERKIN PROCEDURES;429
8.61.3;III. DISCRETIZATION SCHEMES;431
8.61.4;IV. NUMERICAL EXPERIMENTS AND RESULTS;435
8.61.5;REFERENCES;445
8.62;CHAPTER 62. ON A SEMI-COERCIVE QUASI-VARIATIONAL INEQUALITY;446
8.62.1;REFERENCES;451
8.63;CHAPTER 63. A THRESHOLD MODEL OF ANTIGEN ANTIBODY DYNAMICS WITH FADING MEMORY;452
8.63.1;I. INTRODUCTION;452
8.63.2;II. DESCRIPTION OF THE MODEL;452
8.63.3;III. STATEMENT OF RESULTS AND THE SIMULATION;456
8.63.4;IV. PROOFS OF THE THEOREMS;459
8.63.5;REFERENCES;465
8.64;CHAPTER 64. ONE PHENOMENON IN NONLINEAR OSCILLATIONS;468
8.65;CHAPTER 65. TWO FIXED POINT PRINCIPLES;472
8.65.1;REFERENCES;477
8.66;CHAPTER 66. CHEAP SHOOTING METHODS FOR SELF-ADJOINT PROBLEMS USING INITIAL VALUE METHODS;478
8.66.1;INTRODUCTION;478
8.66.2;I. THE BASIC PROBLEM;479
8.66.3;II.
EIGENVALUE PROBLEMS;483
8.66.4;III. CONTROL THEORY;484
8.66.5;IV. NONHOMOGENEOUS
EQUATIONS;484
8.66.6;V. SYSTEMS;485
8.66.7;VI. NONLINEAR EQUATIONS;487
8.66.8;REFERENCES;488
8.67;CHAPTER 67. ON ENTIRE SOLUTIONS IN SOME NONLINEAR FOURTH ORDER ELLIPTIC EQUATIONS;490
8.67.1;I. INTRODUCTION;490
8.67.2;II. LIOUVILLE TYPE RESULT;490
8.67.3;III. CONCLUDING REMARKS;493
8.67.4;REFERENCES;494
8.68;CHAPTER 68. ON THE EXISTENCE OF LARGE AMPLITUDE PLANE-POLARIZED ALFVEN WAVES;496
8.68.1;ACKNOWLEDGMENTS;497
8.68.2;REFERENCES;497
8.69;CHAPTER 69. DIRECT COMPUTER SIMULATION OF NONLINEAR WAVES IN SOLIDS, LIQUIDS AND GASES;498
8.69.1;I. INTRODUCTION;498
8.69.2;II.
TEMPERATURE WAVES I N A HEATED BAR;499
8.69.3;III. ELASTIC VIBRATION;501
8.69.4;IV. SHOCK WAVES;504
8.69.5;V. FREE SURFACE LIQUID WAVES;504
8.69.6;VI. BIOLOGICAL INVERSION OF VOLVOX;507
8.69.7;VII. CONCLUDING REMARKS;507
8.69.8;REFERENCES;509
8.70;CHAPTER 70. FUNCTIONAL EQUATIONS OF FREDHOLM-TYPE AND NONLINEAR BOUNDARY VALUE PROBLEMS;510
8.70.1;INTRODUCTION;510
8.70.2;REFERENCES;516
8.71;CHAPTER 71. ON STRUCTURAL IDENTIFICATION;518
8.71.1;I. INTRODUCTION;518
8.71.2;II. THE TRANSFER MATRIX;519
8.71.3;III. THE DIRECT METHOD OF STRUCTURAL IDENTIFIABILITY;520
8.71.4;IV. APPLICATIONS;521
8.71.5;REFERENCES;523
8.72;CHAPTER 72. RECENT RESULTS FOR WAVE EQUATIONS OF RAYLEIGH AND VAN DER POL TYPE;524
8.72.1;I. INTRODUCTION;524
8.72.2;II. RELATED EQUATIONS;526
8.72.3;III. GLOBAL EXISTENCE;527
8.72.4;IV. BOUNDEDNESS OF SOLUTIONS;529
8.72.5;V. BEHAVIOR AT INFINITY;529
8.72.6;VI. SOME NUMERICAL RESULTS;531
8.72.7;VII. OPEN PROBLEMS;532
8.72.8;REFERENCES;532
8.73;CHAPTER 73. GROUP THEORETICAL METHODS AND THE NONLINEAR SCHRODINGER EQUATION;534
8.73.1;I. INTRODUCTION;534
8.73.2;II. THE DIFFERENTIAL IDEAL DETERMING THE
BACKLUND TRANSFORMATIONS;535
8.73.3;III. INTERACTIONS ALLOWING B.CKLUND TRANSFORMATIONS AND THEIR LIE SYMMETRIES;536
8.73.4;REFERENCES;539
8.74;CHAPTER 74. SMALL DEVIATIONS FROM SYMMETRY IN MODELS IN POPULATION BIOLOGY;540
8.74.1;I. INTRODUCTION;540
8.74.2;II. POPULATION GENETICS EXAMPLE;540
8.74.3;III. DISCUSSION;542
8.74.4;ACKNOWLEDGMENTS;543
8.74.5;REFERENCES;543
8.75;CHAPTER 75. CONTROLLABILITY OF SYSTEMS WHICH GENERATE SOLVABLE LIE ALGEBRAS AND THE ASSOCIATED PROBLEMS IN NONLINEAR FUNCTIONAL ANALYSIS;544
8.75.1;INTRODUCTION;544
8.75.2;I. THE DECOMPOSITION FOR LIE ALGEGRAS SOLVABLE AT A POINT;545
8.75.3;II.
PROBLEMS AND PROPERTIES FOR THE REDUCED SYSTEM;550
8.75.4;REFERENCES;551
8.76;CHAPTER 76. POSITIVE SOLUTIONS OF REACTION-DIFFUSION SYSTEMS WITH NONLINEAR BOUNDARY CONDITIONS AND THE FIXED POINT INDEX;552
8.76.1;I. INTRODUCTION;552
8.76.2;II. A GLOBAL BIFURCATION THEOREM;553
8.76.3;III. APPLICATIONS;555
8.76.4;REFERENCES;561
8.77;CHAPTER 77. ON BIFURCATION FROM INFINITY FOR POSITIVE SOLUTIONS OF SECOND ORDER ELLIPTIC EIGENVALUE PROBLEMS;564
8.77.1;I. STATEMENT OF THE RESULTS;564
8.77.2;II. PROOF OF THEOREM 2;567
8.77.3;ACKNOWLEDGMENTS;571
8.77.4;REFERENCES;571
8.78;CHAPTER 78. THE PRINCIPLE OF BIOLOGICAL EQUIVALENCE AND MATHEMATICAL MODELING IN PHYSIOLOGY;572
8.78.1;I. INTRODUCTION;572
8.78.2;II. MODELS AND MODELING;573
8.78.3;III. VARIABILITY AND THE PRINCIPLE OF BIOLOBICAL EQUIVALENCE;575
8.78.4;IV. MODELING OF EXCHANGE IN CAPILLARY BEDS;576
8.78.5;V. THE CONCENTRATING ACTION OF THE RENAL MEDULA;581
8.78.6;VI. EQUIVALENCE CLASSES OF PROTOTYPE AND OF MODELS;585
8.78.7;REFERENCES;587
8.79;CHAPTER 79. A CLASS OF CONSERVATIVE METHODS FOR THE NUMERICAL SOLUTION OF MULTIPHASE STEFAN PROBLEMS;588
8.79.1;I. DESCRIPTION OF THE PROBLEM;588
8.79.2;II. INTEGRAL RELATION AND CONSERVATION OF ENERGY;590
8.79.3;III. PRINCIPLE OF THE NUMERICAL METHOD;591
8.79.4;IV. APPLICATIONS;595
8.79.5;REFERENCES;595
8.80;CHAPTER 80. CONJUGATES OF DIFFERENTIAL FLOWS II;596
8.80.1;REFERENCES;604
8.81;CHAPTER 81. PROPERTIES OF SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS USING FINITE ELEMENT METHODS;606
8.81.1;I. INTRODUCTION;606
8.81.2;II. SECOND ORDER NONLINEAR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS;606
8.81.3;III. MORE GENERAL NONLINEAR ELLIPTIC EQUATIONS;609
8.82;CHAPTER 82. AN APPROXIMATION SCHEME FOR DELAY EQUATIONS;612
8.82.1;I. INTRODUCTION;612
8.82.2;II. AN APPROXIMATION SCHEME FOR SEMIGROUPS OF NONLINEAR TRANSFORMATIONS;612
8.82.3;III. APPLICATIONS TO FUNCTIONAL DIFFERENTIAL EQUATIONS;616
8.82.4;IV. SPLINE APPROXIMATION;620
8.82.5;REFERENCES;621
8.83;CHAPTER 83. THE CENTER OF A TRANSFORMATION GROUP;624
8.83.1;I. INTRODUCTION;624
8.83.2;II. CENTROL MOTIONS;624
8.83.3;REFERENCES;626
8.83.4;ADDENDUM;626
8.84;CHAPTER 84. A PRIORI BOUNDS IN NONLINEAR SHELL THEORY;628
8.84.1;I. INTRODUCTION;628
8.84.2;II. OPERATOR-THEORETIC FORMULATION OF THE PROBLEM;631
8.84.3;III. A PRIORI BOUNDS;634
8.84.4;REFERENCES;637
8.85;CHAPTER 85. THE RICCATI INTEGRAL EQUATION ARISING IN OPTIMAL CONTROL OF DELAY DIFFERENTIAL EQUATIONS;638
8.85.1;I. INTRODUCTION AND NOTATION;638
8.85.2;II. THE OPTIMAL CONTROL PROBLEM;638
8.85.3;III. APPROXIMATION SCHEMES;642
8.85.4;REFERENCES;645
8.86;CHAPTER 86. EXISTENCE AND ASYMPTOTIC BEHAVIOR OF REACTION
DIFFUSION SYSTEMS VIA COUPLED QUASI-SOLUTIONS;646
8.86.1;I. INTRODUCTION;646
8.86.2;II. NOTATIONS AND DEFINITIONS;646
8.86.3;III.
MONOTONE ITERATIVE TECHNIQUE;648
8.86.4;IV.
ASYMPTOTIC BEHAVIOR OF SOLUTIONS;652
8.86.5;REFERENCES;654
8.87;CHAPTER 87. EMERGENCE OF PERIODIC AND NONPERIODIC MOTIONS IN A BURGERS'
CHANNEL FLOW MODEL;656
8.87.1;I. BURGERS' CHANNEL FLOW MODEL;656
8.87.2;II. DYNAMICAL SYSTEM;657
8.87.3;III. INVISCID NONLINEAR DYNAMICS;658
8.87.4;IV. DYNAMICAL BEHAVIOR OF THE LOWEST-ORDER TRUNCATED SYSTEMS;659
8.87.5;V. CONCLUSIONS;666
8.87.6;REFERENCES;668
8.88;CHAPTER 88. NONHOMOGENEOUS BOUNDARY CONDITIONS FOR GENERALIZED ORDINARY DIFFERENTIAL SUBSPACES;670
8.88.1;I. INTRODUCTION;670
8.88.2;II. NONHOMOGENEOUS BOUNDARY CONDITIONS;670
8.88.3;III. INDICATION OF PROOFS;675
8.88.4;REFERENCES;676
8.89;CHAPTER 89. WEAK CONTINUITY AND COMPACTNESS OF NONLINEAR OPERATORS;678
8.89.1;I. INTRODUCTION;678
8.89.2;II. DEFINITIONS, PRELIMINARY REMARKS, FIRST RESULTS;678
8.89.3;III. WEAK SEQUENTIAL CONTINUITY;679
8.89.4;IV. COMPACT MAPPINGS;679
8.89.5;REFERENCES;680
8.90;CHAPTER 90. ASYMPTOTIC BEHAVIOR OF THE RENEWAL EQUATION ARISING IN THE GURTIN POPULATION MODEL;682
8.90.1;REFERENCES;688
8.91;CHAPTER 91. ASYMPTOTIC BEHAVIOR FOR A STRONGLY DAMPED NONLINEAR WAVE EQUATION;690
8.91.1;I. EXISTENCE, UNIQUENESS, AND COMPACTNESS RESULTS;691
8.91.2;II. BOUNDEDNESS OF ORBITS;694
8.91.3;III. INVARIANT SETS;695
8.91.4;IV. LIMITING BEHAVIOR;695
8.91.5;REFERENCES;696
8.92;CHAPTER 92. NONLINEAR FUNCTIONAL ANALYSIS AND PERIODIC SOLUTIONS OF SEMILINEAR WAVE EQUATIONS;698
8.92.1;I. INTRODUCTION;698
8.92.2;II. THE PERIODIC-DIRICHLET PROBLEM FOR SEMILINEAR WAVE EQUATIONS;698
8.92.3;III. A CONVERGENCE RESULT FOR GALERKIN'S METHOD IN HILBERT SPACE;700
8.92.4;IV.
EXISTENCE THEOREMS WHEN THE NONLINEAR TERM IS OF TYPE m ( L );701
8.92.5;V. A LERAY-SCHAUDER TYPE CONTINUATION THEOREM WHEN THE NONLINEAR TERM IS OF TYPE pm(L);703
8.92.6;REFERENCES;707
8.93;CHAPTER 93. ON SOME SEMILINEAR PROBLEMS WITHOUT COMPACTNESS;710
8.93.1;I. INTRODUCTION;710
8.93.2;II. THE ABSTRACT THEOREMS;710
8.93.3;III. AN A PRIORI ESTIMATE;713
8.93.4;IV. SOME RESULTS FOR HYPERBOLIC PROBLEMS;715
8.93.5;REFERENCES;719
8.94;CHAPTER 94. TRANSFORMATION TECHNIQUES AND NUMERICAL SOLUTION OF MINIMAX PROBLEMS OF OPTIMAL CONTROL: PRELIMINARY RESULTS;720
8.94.1;I. INTRODUCTION;720
8.94.2;II. MINIMAX PROBLEMS;721
8.94.3;III. TRANSFORMATION TECHNIQUES;722
8.94.4;IV. EXAMPLES;724
8.94.5;V. EXPERIMENTAL CONDITIONS;726
8.94.6;VI. NUMERICAL RESULTS;726
8.94.7;VII. CONCLUSIONS;727
8.94.8;REFERENCES;727
8.95;CHAPTER 95. BIFURCATION OF CLOSED PATHS FROM A CLOSED PATH IN R2;730
8.95.1;SECTION I;730
8.95.2;SECTION II;731
8.95.3;SECTION
III;735
8.95.4;REFERENCES;738
8.96;CHAPTER 96. LOCAL ESTIMATES AND THE EXISTENCE OF MULTIPLE SOLUTIONS TO NONLINEAR ELLIPTIC PROBLEMS;740
8.96.1;I. PRELIMINARIES;741
8.96.2;II. EXISTENCE RESULTS DERIVED FROM THE LOCAL BEHAVIOR OF g;743
8.96.3;III. THE SPECIAL CASE WHEN . . 1;747
8.96.4;REFERENCES;749
8.97;CHAPTER 97. SEQUENCE OF ITERATES IN LOCALLY CONVEX SPACES;752
8.97.1;REFERENCES;763
8.98;CHAPTER 98. ON WELL-POSED AND ILL-POSED EXTREMAL PROBLEMS;764
8.98.1;REFERENCES;770
8.99;CHAPTER 99. A NONLINEAR VOLTERRA EQUATION IN VISCOELASTICITY;774
8.99.1;ABSTRACT;774
8.100;CHAPTER 100. A MODEL OF WHOLE MUSCLES INCORPORATING FUNCTIONALLY IMPORTANT NONLINEARITIES;776
8.100.1;I. INTRODUCTION;776
8.100.2;II. REFORMULATION OF MUSCLE EQUATIONS;780
8.100.3;III. ISOLATED MUSCLES;783
8.100.4;IV. SOLUTION OF THE NONLINEAR MUSCLE EQUATIONS;787
8.100.5;V. COMPUTER SIMULATIONS OF MUSCLE MODEL;788
8.100.6;REFERENCES;792
8.101;CHAPTER 101. ASYMPTOTIC LIMIT AND BLOWING-UP BEHAVIOR OF SOLUTIONS FOR A REACTION-DIFFUSION SYSTEM;794
8.101.1;I. INTRODUCTION;794
8.101.2;II. ASYMPTOTIC LIMIT AND STABILITY;796
8.101.3;III. THE BLOWING-UP PROPERTY OF THE SOLUTION;802
8.101.4;REFERENCES;806
8.102;CHAPTER 102. LARGE-SCALE EIGENMODES OF A TURBULENT FLAT-PLATE BOUNDARY LAYER;808
8.102.1;I . OVERVIEW;808
8.102.2;II. WHAT IS TURBULENCE?;809
8.102.3;III. LUMLEY'S STABILITY METHOD;810
8.102.4;IV. APPLICATION TO THE FLAT-PLATE;811
8.102.5;V. SOLUTION OF REDUCED LUMLEY EQUATIONS;813
8.102.6;VI. NUMERIC RESULTS;814
8.102.7;VII. CONCLUSIONS;816
8.102.8;VIII. CONJECTURE;816
8.102.9;REFERENCES;818
8.103;CHAPTER
103. NONLINEAR OSCILLATIONS IN TRIGGERED SYSTEMS;820
8.103.1;I. INTRODUCTION;820
8.103.2;II. THE SEMILINEARIZED APPROXIMATION;821
8.103.3;III. STRONGLY OSCILLATING SYSTEMS;822
8.103.4;IV. CONDITIONS FOR STRONG OSCILLATIONS;824
8.103.5;V. CONSEQUENCES IN THE PROBLEM OF MUTABILITY;825
8.103.6;VI.
NAXINAL STRUCTURES OF MUTABLE SYSTEMS;828
8.103.7;APPENDIX I. PROOF OF LEMMA 3.3;829
8.103.8;APPENDIX II. PROOF OF LEMMA 4.3;834
8.103.9;REFERENCES;835
8.104;CHAPTER 104. BEHAVIOR OF SOLUTIONS OF SOME SPATIALLY DEPENDENT INTEGRODIFFERENTIAL EQUATIONS;836
8.104.1;I. INTRODUCTION;836
8.104.2;II. THE EQUATION AND THE ABSTRACT THEORY;836
8.104.3;III. STATEMENTS OF THE RESULTS;839
8.104.4;IV. PROOF OF THEOREM 1;840
8.104.5;V. APPLICATIONS OF THEOREM 1;841
8.104.6;REFERENCES;844
8.105;CHAPTER 105. NONLINEAR EQUATIONS AND PASSIVE NETWORKS;846
8.105.1;SUMMARY;846
8.105.2;REFERENCES;846
8.106;CHAPTER 106. A BRIOT-BOUQUET EQUATION AND SUBORDINATION;848
8.106.1;I. INTRODUCTION;848
8.106.2;II. PRELIMINARIES;848
8.106.3;III. MAIN RESULTS;849
8.106.4;IV. CONCLUSION;851
8.106.5;REFERENCES;851
8.107;CHAPTER 107. GLOBAL STABILITY OF BALANCED PREDATOR-PREY SYSTEMS;852
8.108;CHAPTER 108. NONLINEAR SEMIGROUPS, ACCRETIVE OPERATORS, AND APPLICATIONS;858
8.108.1;REFERENCES;864
8.109;CHAPTER 109. ACTIVATION-INHIBITION PATTERNS;866
8.109.1;REFERENCES;872
8.110;CHAPTER 110. ON THE DEVELOPMENT OF AN INTRINSIC DEFINITION OF THE LERAY-SCHAUDER DEGREE;874
8.110.1;I. INTRODUCTION;874
8.110.2;II. THE THEORY OF NAGUMO FOR THE FINITE DIMENSIONAL CASE;874
8.110.3;III. THE PROBLEM IN BANACH SPACE;876
8.110.4;IV. THE DEFINITION OF d(f,O,y ) FOR A REGULAR VALUE
y0;876
8.110.5;V. THE DEFINITION OF d(f, O, y0) FOR A SINGULAR VALUE
y0;879
8.110.6;REFERENCES;884
8.111;CHAPTER 111. SOME RECENT DEVELOPMENTS IN THE INFINITE TIME OPTIMAL CONTROL PROBLEM;886
8.111.1;I. INTRODUCTION;886
8.111.2;II. OPTIMALITY IN
(0,8);887
8.111.3;III. THE DETERMINING SET FOR THE ADJOINT VECTOR;889
8.111.4;IV. PERIODIC OPTIMAL SOLUTIONS;893
8.111.5;V. OTHER RESULTS;894
8.111.6;REFERENCES;894
8.112;CHAPTER 112. ON SOME NONLINEAR PROBLEMS OF ANALYTICAL MECHANICS AND THEORY OF STABILITY;896
8.112.1;REFERENCES;908
8.113;CHAPTER 113. PERIODIC ENVIRONMENTS, HARVESTING, AND A RICCATI EQUATION;910
8.113.1;I. DEDICATION;910
8.113.2;II. INTRODUCTION;910
8.113.3;III. THE PERIODIC MODEL;910
8.113.4;IV. SOME FURTHER ANALYSIS;912
8.113.5;REFERENCES;913
8.114;CHAPTER 114. A HEURISTIC WAY OF FINDING LINEAR PROBLEMS FROM SOLITON SOLUTIONS OF NONLINEAR WAVE EQUATIONS;914
8.114.1;I. INTRODUCTION;914
8.114.2;II. SOLUTIONS OF THE GEL'FAND-LEVITAN EQUATION;915
8.114.3;III. SOLITON SOLUTIONS OF THE INTERMEDIATE LONG WAVE EQUATION;915
8.114.4;IV. LINEAR PROBLEM FOR THE INTERMEDIATE LONG WAVE EQUATION;917
8.114.5;V. CONCLUDING REMARKS;919
8.114.6;REFERENCES;919
8.115;CHAPTER 115. EXISTENCE OF CARATHEODORY-MARTIN EVOLUTIONS;922
8.115.1;I. INTRODUCTION;922
8.115.2;II. A PRIORI ESTIMATES;924
8.115.3;III. APPROXIMATE SOLUTIONS;925
8.115.4;REFERENCES;926
8.115.5;ADDENDUM;927
8.116;CHAPTER 116. ESTIMATES FOR VECTOR-VALUED ELLIPTIC-PARABOLIC PROBLEMS OF THE SECOND ORDER;928
8.116.1;I. ORDINARY DIFFERENTIAL OPERATORS;929
8.116.2;II. ELLIPTIC DIFFERENTIAL OPERATORS;931
8.116.3;III. ABSTRACT DIFFERENTIAL OPERATORS;932
8.116.4;IV. VARIOUS GENERALIZATIONS;934
8.116.5;V. EXISTENCE AND ESTIMATION;936
8.116.6;REFERENCES;937
8.117;CHAPTER 117. QUALITATIVE BEHAVIOR OF ORDINARY DIFFERENTIAL EQUATIONS OF THE QUASILINEAR AND RELATED TYPES;938
8.117.1;REFERENCES;941
8.118;CHAPTER 118. ON THE EXISTENCE OF LYAPUNOV FUNCTIONS IN GENERAL SYSTEMS;944
8.118.1;INTRODUCTION;944
8.118.2;I. ASYMPTOTICITY AND AL2 FUNCTIONS;945
8.118.3;II. THE EXISTENCE OF AN AL2
FUNCTION;948
8.118.4;REFERENCES;952
8.119;CHAPTER 119. DIFFERENTIAL MODULES AND THEOREM OF HUKUHARA-TURRITTIN;954
8.119.1;I. THEOREM OF
HUKUHARA–TURRITTIN;954
8.119.2;II. DIFFERENTIAL MODULES;957
8.119.3;III.
CYCLIC VECTORS;958
8.119.4;IV.
FACTORIZATION;959
8.119.5;V. FUCHSIAN MODULES;962
8.119.6;VI.
THE FINAL CONCLUSION;963
8.119.7;REFERENCES;964
8.120;CHAPTER 120. TIME-DEPENDENT INTEGRODIFFERENTIAL EQUATIONS IN BANACH SPACES;966
8.120.1;I. INTRODUCTION;966
8.120.2;II. CONTINUOUS INTERPOLATION SPACES AND SHARP REGULARITY PROPERTY;966
8.120.3;III. EXISTENCE AND UNIQUENESS RESULTS;967
8.120.4;IV. THE LINEAR CASE;969
8.120.5;V. AN EXAMPLE;972
8.120.6;REFERENCES;973
8.121;CHAPTER 121. SOLVABILITY OF NONLINEAR ODD-ORDERED DIFFERENTIAL EQUATIONS USING
K-MONOTONICITY;974
8.121.1;I. INTRODUCTION;974
8.121.2;II.
A NONRESONANT PROBLEM;975
8.121.3;III. PERIODIC SOLUTIONS;978
8.121.4;REFERENCES;982
8.122;CHAPTER 122. MONOTONICITY AND UPPER SEMICONTINUITY OF MULTIFUNCTIONS;984
8.122.1;I.
INTRODUCTION;984
8.122.2;II. NOTATIONS AND PRELIMINARIES;985
8.122.3;III. GENERALIZED MONOTONICITY;986
8.122.4;IV. EXAMPLES;987
8.122.5;REFERENCES;989
8.123;CHAPTER 123. CLASSIFICATION OF CERTAIN CONTINUOUS FLOWS;992
8.123.1;I. INTRODUCTION;992
8.123.2;II. PRELIMINARY RESULTS AND NOTATIONS;992
8.123.3;III. FLOWS WHERE PROLONGATION AND LIMIT SETS COINCIDE;993
8.123.4;REFERENCES;997
8.124;CHAPTER 124. PHARMACOKINETIC SYSTEMS ANALYSIS: SOME NEW FORMULATIONS;998
8.124.1;I. INTRODUCTION;998
8.124.2;II. TIME DELAY EFFECTS;1000
8.124.3;III. TIME VARYING RATE COEFFICIENTS;1002
8.124.4;IV. A PARAMETRIC APPROACH TO ESTIMATING TIME DEPENDENT RATE COEFFICIENTS;1003
8.124.5;REFERENCES;1005
8.125;CHAPTER 125. FUNCTIONAL DIFFERENCE EQUATIONS AND AN EPIDEMIC MODEL;1006
8.125.1;ACKNOWLEDGMENTS;1011
8.125.2;REFERENCES;1011
8.125.3;ADDENDUM;1012
8.126;CHAPTER 126. NECESSARY AND SUFFICIENT CONDITIONS FOR CONTINUOUS DEPENDENCE OF FIXED POINTS OF
a-CONDENSING MAPS;1014
8.126.1;REFERENCES;1016
8.127;CHAPTER 127. DIFFERENTIAL INEQUALITIES - IN MEMORIAM OF JACEK SZARSKI (1921-1980);1018
8.127.1;A SHORT NOTE;1018
8.128;CHAPTER 128. ASYMPTOTIC CONDITIONS FOR FORCED NONLINEAR OSCILLATIONS;1020
8.128.1;REFERENCES;1022
8.129;CHAPTER 129. LYAPUNOV FUNCTIONS FOR EVOLUTION EQUATIONS IN HILBERT SPACES VIA THE OPERATORIAL RICCATI EQUATION;1024
8.129.1;REFERENCES;1028
8.130;CHAPTER 130. MODELS OF CELL KINETICS AND THE ESTIMATION OF MACROMOLECULAR SYNTHESIS RATES;1030
8.130.1;I. ONE DIMENSIONAL STATIONARY CASE;1036
8.130.2;II. ONE DIMENSIONAL QUASI-TRANSIENT CASE;1038
8.130.3;III. GENERAL
m-DIMENSIONAL STATIONARY CASE;1039
8.130.4;IV. NONLINEAR PROBLEMS;1041
8.130.5;REFERENCES;1041
8.131;CHAPTER 131. DISTRIBUTIONAL AND ANALYTIC SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS;1044
8.131.1;REFERENCES;1047
8.132;CHAPTER 132. MODELING CELLULAR SYSTEMS AND AGING PROCESSES: II. SOME THOUGHTS ON DESCRIBING AN ASYNCHRONOUSLY DIVIDING CELLULAR SYSTEM;1050
8.132.1;I. INTRODUCTION, HISTORICAL BACKGROUND, AND PRELIMINARIES;1050
8.132.2;II. CONSTRUCTING AN ASYNCHRONOUS CELL SYSTEM MODEL;1051
8.132.3;III. FURTHER GENERALIZATIONS;1059
8.132.4;REFERENCES;1060