Contributions to Nonlinear Analysis A Tribute to D.G. de Figueiredo on the Occasion of his 70th Birthday
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Thierry Cazenave, David Costa, Orlando Lopes, Raúl Manásevich et al.
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Thierry Cazenave, David Costa, Orlando Lopes, Raúl Manásevich, Paul Rabinowitz, Bernhard Ruf, Carlos
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Contributions to Nonlinear Analysis A Tribute to D.G. de Figueiredo on the Occasion of his 70th Birthday
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Birkhäuser Basel
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9783764374013
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1
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CHF 85.50
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Analysis
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English
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520
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Wasserzeichen/DRM
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PC/MAC/eReader/Tablet
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PDF
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.
Dedication
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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
