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Contributions to Nonlinear Analysis

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

  • Book
  • © 2006

Overview

Editors:
  1. Thierry Cazenave

    1. Laboratoire Jacques-Louis Lions B.C. 187, Université Pierre et Marie Curie, Paris Cedex 05, France

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  2. David Costa

    1. Department of Mathematical Sciences, University of Nevada, Las Vegas, USA

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  3. Orlando Lopes

    1. Instituto de Matemática, UNICAMP - IMECC, Campinas, SP, Brasil

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  4. Raúl Manásevich

    1. Departamento de Ingenieria Matemática Facultad de Ciencias Fisicas y Matemáticas, Universidad de Chile, Santiago, Chile

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  5. Paul Rabinowitz

    1. Mathematics Department, University of Wisconsin-Madison, Madison, USA

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  6. Bernhard Ruf

    1. Dipartimento di Matematica, Università degli Studi, Milano, Italy

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  7. Carlos Tomei

    1. Departamento de Matemática, PUC Rio, Gávea - Rio de Janeiro, Brasil

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  • State of the art in the fields of nonlinear analysis and nonlinear differential equations
  • A tribute to the distinguished mathematician D.G. de Figueiredo
  • Includes supplementary material: sn.pub/extras

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 66)

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Table of contents (34 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Remarks on a Class of Neumann Problems Involving Critical Exponents

    • Emerson A. M. Abreu, Paulo Cesar Carrião, Olimpio Hiroshi Miyagaki
    Pages 1-15

  3. Existence of Solutions for a Class of Problems in IR N Involving the p(x)-Laplacian

    • Claudianor O. Alves, Marco A.S. Souto
    Pages 17-32

  4. A Unitarian Approach to Classical Electrodynamics: The Semilinear Maxwell Equations

    • Vieri Benci, Donato Fortunato
    Pages 33-52

  5. Existence of Solutions for the Nonlinear Schrödinger Equation with V (∞) = 0

    • Vieri Benci, Carlo R. Grisanti, Anna Maria Micheletti
    Pages 53-65

  6. Asymptotic Behavior of a Bernoulli-Euler Type Equation with Nonlinear Localized Damping

    • R.C. Charão, E. Bisognin, V. Bisognin, A.F. Pazoto
    Pages 67-91

  7. T-minima

    • Lucio Boccardo
    Pages 93-103

  8. A Note on Heteroclinic Solutions of Mountain Pass Type for a Class of Nonlinear Elliptic PDE’s

    • Sergey Bolotin, Paul H. Rabinowitz
    Pages 105-114

  9. Existence of Multiple Solutions for Quasilinear Equations via Fibering Method

    • Yuri Bozhkov, Enzo Mitidieri
    Pages 115-134

  10. Symmetry of Solutions of a Semilinear Elliptic Problem in an Annulus

    • Daniele Castorina, Filomena Pacella
    Pages 135-147

  11. Construction of a Radial Solution to a Superlinear Dirichlet Problem that Changes Sign Exactly Once

    • Alfonso Castro, Jorge Cossio
    Pages 149-160

  12. Global Solvability and Asymptotic Stability for the Wave Equation with Nonlinear Boundary Damping and Source Term

    • M.M. Cavalcanti, V.N. Domingos Cavalcanti, J.A. Soriano
    Pages 161-184

  13. Multiscale Asymptotic Behavior of a Solution of the Heat Equation on \( \mathbb{R}^N \)

    • Thierry Cazenave, Flávio Dickstein, Fred B. Weissler
    Pages 185-194

  14. Positive Solutions for a Class of Nonlocal Elliptic Problems

    • F. J. S. A. Corrêa, S. D. B. Menezes
    Pages 195-206

  15. On a Class of Critical Elliptic Equations of Caffarelli-Kohn-Nirenberg Type

    • David G. Costa, Olímpio H. Miyagaki
    Pages 207-220

  16. Existence and Number of Solutions for a Class of Semilinear Schrödinger Equations

    • Yanheng Ding, Andrzej Szulkin
    Pages 221-231

  17. Multiparameter Elliptic Equations in Annular Domains

    • João Marcos do Ó, Sebastián Lorca, Pedro Ubilla
    Pages 233-245

  18. Variational Principle for the Seiberg-Witten Equations

    • Celso Melchiades Doria
    Pages 247-261

  19. Some Recent Results on Equations Involving the Pucci’s Extremal Operators

    • Patricio Felmer, Alexander Quaas
    Pages 263-281

  20. Principal Eigenvalue in an Unbounded Domain and a Weighted Poincaré Inequality

    • Jacqueline Fleckinger-Pellé, Jean-Pierre Gossez, François de Thélin
    Pages 283-296
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Keywords

About this book

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.

Editors and Affiliations

  • Laboratoire Jacques-Louis Lions B.C. 187, Université Pierre et Marie Curie, Paris Cedex 05, France

    Thierry Cazenave

  • Department of Mathematical Sciences, University of Nevada, Las Vegas, USA

    David Costa

  • Instituto de Matemática, UNICAMP - IMECC, Campinas, SP, Brasil

    Orlando Lopes

  • Departamento de Ingenieria Matemática Facultad de Ciencias Fisicas y Matemáticas, Universidad de Chile, Santiago, Chile

    Raúl Manásevich

  • Mathematics Department, University of Wisconsin-Madison, Madison, USA

    Paul Rabinowitz

  • Dipartimento di Matematica, Università degli Studi, Milano, Italy

    Bernhard Ruf

  • Departamento de Matemática, PUC Rio, Gávea - Rio de Janeiro, Brasil

    Carlos Tomei

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