Contributions to Nonlinear Analysis (eBook)

A Tribute to D.G. de Figueiredo on the Occasion of his 70th Birthday

Thierry Cazenave, David Costa, Orlando Lopes, Raúl Manásevich, Paul Rabinowitz, Bernhard Ruf, Carlos Tomei (Herausgeber)

eBook Download: PDF

2007 | 2006
XII, 520 Seiten
Springer Basel (Verlag)
978-3-7643-7401-3 (ISBN)

Infos

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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 10.8.2007
• Reihe/Serie: Progress in Nonlinear Differential Equations and Their Applications
• Reihe/Serie: Progress in Nonlinear Differential Equations and Their Applications
• Zusatzinfo: XII, 520 p.
• Verlagsort: Basel
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Technik
• Schlagworte: Calculus • hyperbolic equation • Maxwell's equations • Nonlinear Equations • partial differential equation • Partial differential equations • wave equation
• ISBN-10: 3-7643-7401-2 / 3764374012
• ISBN-13: 978-3-7643-7401-3 / 9783764374013