Cazenave / Costa / Lopes Contributions to Nonlinear Analysis

A Tribute to D.G. de Figueiredo on the Occasion of his 70th Birthday
1. Auflage 2007
ISBN: 978-3-7643-7401-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 66, 520 Seiten

Reihe: Progress in Nonlinear Differential Equations and Their Applications

This paper is concerned with the existence and uniform decay rates of solutions of the waveequation with a sourceterm and subject to nonlinear boundary damping ? ? u ?? u =|u| u in ? ×(0,+?) ? tt ? ? ? ? u=0 on ? ×(0,+?) 0 (1. 1) ? ? u+g(u)=0 on ? ×(0,+?) ? t 1 ? ? ? ? 0 1 u(x,0) = u (x); u (x,0) = u (x),x? ? , t n where ? is a bounded domain of R ,n? 1, with a smooth boundary ? = ? ?? . 0 1 Here, ? and ? are closed and disjoint and ? represents the unit outward normal 0 1 to ?. Problems like (1. 1), more precisely, ? u ?? u =?f (u)in? ×(0,+?) ? tt 0 ? ? ? ? u=0 on ? ×(0,+?) 0 (1. 2) ? ? u =?g(u )?f (u)on? ×(0,+?) ? t 1 1 ? ? ? ? 0 1 u(x,0) = u (x); u (x,0) = u (x),x? ? , t were widely studied in the literature, mainly when f =0,see[6,13,22]anda 1 long list of references therein. When f =0and f = 0 this kind of problem was 0 1 well studied by Lasiecka and Tataru [15] for a very general model of nonlinear functions f (s),i=0,1, but assuming that f (s)s? 0, that is, f represents, for i i i each i, an attractive force.

Autoren/Hrsg.

Cazenave, Thierry

Costa, David

Lopes, Orlando

Manásevich, Raúl

Rabinowitz, Paul

Ruf, Bernhard

Tomei, Carlos

Carlos,

Inhaltsverzeichnis

1;Dedication;10
2;On Djairo de Figueiredo. A Mathematician;11
3;Remarks on a Class of Neumann Problems Involving Critical Exponents;13
4;Existence of Solutions for a Class of Problems;28
5;A Unitarian Approach to Classical Electrodynamics: The Semilinear Maxwell Equations;44
6;Existence of Solutions for the Nonlinear;64
7;Schr¨ odinger Equation with;64
8;Asymptotic Behavior of a Bernoulli–Euler Type Equation with Nonlinear Localized Damping;77
9;T-minima;102
10;A Note on Heteroclinic Solutions of Mountain Pass Type for a Class of Nonlinear Elliptic PDE’s;113
11;Existence of Multiple Solutions for Quasilinear Equations via Fibering Method;123
12;Symmetry of Solutions of a Semilinear Elliptic Problem in an Annulus;143
13;Construction of a Radial Solution to a Superlinear Dirichlet Problem that Changes Sign Exactly Once;156
14;Global Solvability and Asymptotic Stability for the Wave Equation with Nonlinear Boundary Damping and Source Term;168
15;Multiscale Asymptotic Behavior of a Solution of the Heat Equation on;192
16;Positive Solutions for a Class of Nonlocal Elliptic Problems;202
17;On a Class of Critical Elliptic Equations of Caffarelli- Kohn- Nirenberg Type;214
18;Existence and Number of Solutions for a Class of Semilinear Schrödinger Equations;228
19;Multiparameter Elliptic Equations in Annular Domains;239
20;Variational Principle for the Seiberg– Witten Equations;252
21;Some Recent Results on Equations Involving the Pucci’s Extremal Operators;267
22;Principal Eigenvalue in an Unbounded Domain and a Weighted Poincar ´ e Inequality;286
23;Uniform Stabilization for a Hyperbolic Equation with Acoustic Boundary Conditions in Simple Connected Domains;300
24;Some Remarks on Semilinear Resonant Elliptic Problems;316
25;Remarks on Regularity Theorems for Solutions to Elliptic Equations via the Ultracontractivity of the Heat Semigroup;324
26;2d Ladyzhenskaya–Solonnikov Problem for Inhomogeneous Fluids;354
27;Generalization of a Well-known Inequality;368
28;Nonexistence of Nontrivial Solutions for Supercritical Equations of Mixed Elliptic- Hyperbolic Type;374
29;On the Shape of Least-Energy Solutions to a Quasilinear Elliptic Equation Involving Critical Sobolev Exponents;394
30;A-priori Bounds and Positive Solutions to a Class of Quasilinear Elliptic Equations;410
31;The Role of the Equal-Area Condition in Internal and Superficial Layered Solutions to Some Nonlinear Boundary Value Elliptic Problems;417
32;Some Recent Results Regarding Symmetry and Symmetry- breaking Properties of Optimal Composite Membranes;430
33;Generic Simplicity for the Solutions of a Nonlinear Plate Equation;444
34;An Estimate for the Blow-up Time in Terms of the Initial Data;465
35;Lorentz Spaces and Nonlinear Elliptic Systems;470
36;The Topology of Critical Sets of Some Ordinary Differential Operators;489
37;A Note on the Superlinear Ambrosetti–Prodi Type Problem in a Ball;503