Buch, Englisch, 342 Seiten, Format (B × H): 170 mm x 244 mm, Gewicht: 615 g
ISBN: 978-94-009-9546-8
Verlag: Springer
The progress in nonlinear functional analysis has allowed the study of many nonlinear problems in mathematical physics. This book provides basic methods and results for the investigation of the special problems in this area. The connection between nonlinear analysis and convex analysis gave rise to the important field of monotone operators from a Banach space into its dual space. These mappings extend the properties of compact operators to the infinite-dimensional case. Generalizations of monotone operators are termed mappings of monotone type. Among these, in the last decade, the pseudo-monotone operators and the mappings of type (M) have provided a more proper tool for solving large classes of nonlinear differential and integral equations. The text dwells upon essentially four interrelated topics: Nonlinear mappings of mono tone type, Hammerstein equations, Odd operators and Variational problems. To make the approach easier, we have compiled some basic results on the topological degree and on the Sobolev spaces. In the applications we restrict our discussion to the existence of solutions for nonlinear elliptic equations. The present English editIOn was written starting from the Romanian book "Operatori neliniari" (Nonlinear Mappings) by the first author and his lectures delivered at the Universities of Bucharest and Rome. The improved final form of this book is the result of the joint work of the authors.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
I. Background in Functional Analysis.- 1. Topology and measure.- 2. Convex analysis.- 3. Related topics and exercises.- II. Methods of Compactness.- 1. Compact operators.- 2. Sobolev spaces.- 3. Theory of topological degree.- 4. Related topics and exercises.- III. Nonlinear Mappings of Monotone Type.- 1. Pseudo-monotone mappings.- 2. Monotone mappings.- 3. Perturbation of maximal monotone mappings.- 4. Noncoercive operators.- 5. Mappings of type (M).- 6. Related topics and exercises.- IV. Hammerstein Equations.- 1. The Nemitskyi operator.- 2. Abstract Hammerstein equations.- 3. Angle-bounded mappings.- 4. Variational methods.- 5. Related topics and exercises.- V. Homotopy Arguments.- 1. Odd mappings.- 2. Eigenvalue problems for maximal monotone operators.- 3. Range of sums of monotone mappings.- 4. Related topics and exercises.- VI. Variational Problems and Inequalities.- 1. Variational inequalities.- 2. Variational boundary-value problems.- 3. Strongly nonlinear problems.- 4. Other methods.- 5. Boundary-value problems in unbounded domains.- 6. Related topics and exercises.- Suggestions for further study.- References.
