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

516 Pages·2006·3.698 MB·English

by  Emerson A. M. Abreu, Paulo Cesar Carrião (auth.), Thierry Cazenave, David Costa, Orlando Lopes, Raúl Manásevich, Paul Rabinowitz, Bernhard Ruf, Carlos Tomei (eds.)

Progress in Nonlinear Differential Equations
and Their Applications
Volume 66
Editor
Haim Brezis
Université Pierre et Marie Curie
Paris
and
Rutgers University
New Brunswick, N.J.
Editorial Board
Antonio Ambrosetti, Scuola Internazionale Superiore di Studi Avanzati, Trieste
A. Bahri, Rutgers University, New Brunswick
Felix Browder, Rutgers University, New Brunswick
Luis Cafarelli, Institute for Advanced Study, Princeton
Lawrence C. Evans, University of California, Berkeley
Mariano Giaquinta, University of Pisa
David Kinderlehrer, Carnegie-Mellon University, Pittsburgh
Sergiu Klainerman, Princeton University
Robert Kohn, New York University
P.L. Lions, University of Paris IX
Jean Mahwin, Université Catholique de Louvain
Louis Nirenberg, New York University
Lambertus Peletier, University of Leiden
Paul Rabinowitz, University of Wisconsin, Madison
John Toland, University of Bath
Contributions to
Nonlinear Analysis
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
Editors
Birkhäuser
Basel Boston Berlin
(cid:404) (cid:404)
Editors:
Thierry Cazenave Paul Rabinowitz
Laboratoire Jacques-Louis Lions University of Wisconsin-Madison
B.C. 187 Mathematics Department
Université Pierre et Marie Curie 480 Lincoln Dr
4, place Jussieu Madison WI 53706-1388, USA
75252 Paris Cedex 05, France e-mail: [email protected]
e-mail: [email protected]
Bernhard Ruf
David Costa Dipartimento di Matematica
Department of Mathematical Sciences Università degli Studi
University of Nevada Via Saldini 50
Las Vegas, NV 89154-4020, USA 20133 Milano, Italy
e-mail: [email protected] e-mail: [email protected]
Orlando Lopes Carlos Tomei
Instituto de Matemática Departamento de Matemática
UNICAMP - IMECC PUC Rio
Caixa Postal: 6065 Rua Marquês de São Vicente, 225
13083-859 Campinas, SP, Brasil Edifício Cardeal Leme
e-mail: [email protected] Gávea - Rio de Janeiro, 22453-900, Brasil
e-mail: [email protected]
Raúl Manásevich
Departamento de Ingenieria Matemática
Facultad de Ciencias Fisicas y Matemáticas
Universidad de Chile
Casilla 170, Correo 3, Santiago, Chile.
e-mail: [email protected]
2000 Mathematics Subject Classifi cation 35, 49, 34
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ISBN 3-7643-7149-8 Birkhäuser Verlag, Basel – Boston – Berlin
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Contents
Dedication....................................................................ix
J. Palis
On Djairo de Figueiredo. A Mathematician ..............................xi
E.A.M. Abreu, P.C. Carria˜o and O.H. Miyagaki
Remarks on a Class of Neumann Problems Involving Critical Exponents .1
C.O. Alves and M.A.S. Souto
Existence of Solutions for a Class of Problems in IRN Involving
the p(x)-Laplacian ......................................................17
V. Benci and D. Fortunato
A Unitarian Approach to Classical Electrodynamics:
The Semilinear Maxwell Equations .....................................33
V. Benci, C.R. Grisanti and A.M. Micheletti
Existence of Solutions for the Nonlinear Schro¨dinger Equation
with V(∞)=0 .........................................................53
R.C. Chara˜o, E. Bisognin, V. Bisognin and A.F. Pazoto
Asymptotic Behavior of a Bernoulli–Euler Type Equation with
Nonlinear Localized Damping ...........................................67
L. Boccardo
T-minima ..............................................................93
S. Bolotin and P.H. Rabinowitz
A Note on Heteroclinic Solutions of Mountain Pass Type
for a Class of Nonlinear Elliptic PDE’s ................................105
Y. Bozhkov and E. Mitidieri
Existence of Multiple Solutions for Quasilinear Equations
via Fibering Method ..................................................115
D. Castorina and F. Pacella
Symmetry of Solutions of a Semilinear Elliptic Problem
in an Annulus .........................................................135
A. Castro and J. Cossio
Construction of a Radial Solution to a Superlinear Dirichlet Problem
that Changes Sign Exactly Once ......................................149
vi Contents
M.M. Cavalcanti, V.N. Domingos Cavalcanti and J.A. Soriano
Global Solvability and Asymptotic Stability for the Wave Equation
with Nonlinear Boundary Damping and Source Term ..................161
T. Cazenave, F. Dickstein and F.B. Weissler
Multiscale Asymptotic Behavior of a Solution of the Heat Equation
on RN ................................................................185
F.J.S.A. Corrˆea and S.D.B. Menezes
Positive Solutions for a Class of Nonlocal Elliptic Problems ............195
D.G. Costa and O.H. Miyagaki
On a Class of Critical Elliptic Equations of
Caffarelli-Kohn-NirenbergType .......................................207
Y. Ding and A. Szulkin
Existence and Number of Solutions for a Class of Semilinear
Schro¨dinger Equations .................................................221
J.M. do O´, S. Lorca and P. Ubilla
Multiparameter Elliptic Equations in Annular Domains ................233
C.M. Doria
Variational Principle for the Seiberg–Witten Equations ................247
P. Felmer and A. Quaas
Some Recent Results on Equations Involving the Pucci’s Extremal
Operators .............................................................263
J. Fleckinger-Pell´e, J.-P. Gossez and F. de Th´elin
Principal Eigenvalue in an Unbounded Domain and a Weighted
Poincar´eInequality ....................................................283
C.L. Frota and N.A. Larkin
Uniform Stabilization for a Hyperbolic Equation with Acoustic
Boundary Conditions in Simple Connected Domains ...................297
J.V. Goncalves and C.A. Santos
Some Remarks on Semilinear Resonant Elliptic Problems ..............313
O. Kavian
Remarks on Regularity Theorems for Solutions to Elliptic Equations
via the Ultracontractivity of the Heat Semigroup ......................321
Contents vii
F. Ammar Khodja and M.M. Santos
2d Ladyzhenskaya–SolonnikovProblem for Inhomogeneous Fluids ......351
Y.Y. Li and L. Nirenberg
Generalization of a Well-known Inequality .............................365
D. Lupo, K.R. Payne and N.I. Popivanov
Nonexistence of Nontrivial Solutions for Supercritical Equations
of Mixed Elliptic-Hyperbolic Type .....................................371
E.S. Medeiros
On the Shape of Least-Energy Solutions to a Quasilinear Elliptic
Equation Involving Critical Sobolev Exponents ........................391
M. Montenegro and F.O.V. de Paiva
A-priori Bounds and Positive Solutions to a Class of Quasilinear
Elliptic Equations .....................................................407
A.S. do Nascimento and R.J. de Moura
The Role of the Equal-Area Condition in Internal and Superficial
Layered Solutions to Some Nonlinear Boundary Value Elliptic
Problems ..............................................................415
R.H.L. Pedrosa
Some Recent Results Regarding Symmetry and Symmetry-breaking
Properties of Optimal Composite Membranes ..........................429
A.L. Pereira and M.C. Pereira
Generic Simplicity for the Solutions of a Nonlinear Plate Equation .....443
J.D. Rossi
An Estimate for the Blow-up Time in Terms of the Initial Data ........465
B. Ruf
Lorentz Spaces and Nonlinear Elliptic Systems ........................471
N.C. Saldanha and C. Tomei
The Topology of Critical Sets of Some Ordinary Differential Operators .491
P.N. Srikanth and S. Santra
A Note on the Superlinear Ambrosetti–Prodi Type Problem in a Ball ..505

Dedication
This volume is dedicated to Djairo G. de Figueiredo on the occasion
of his 70th birthday.
In January 2003 David Costa, Orlando Lopes and Carlos Tomei, colleagues and
friends of Djairo, invited us to join the organizing committee for a Workshop on
Nonlinear Differential Equations, sending us the following message:
Djairo’scareerisaremarkableexamplefortheBrazilian community.Weareproud
of his mathematical achievements and his ability to develop so many successors,
through systematicdedication toresearch, advising activities and academic orches-
tration. Djairo is always organizing seminars and conferences and is constantly
willing to help individuals and the community. It is about time that he should
enjoy a meeting without having to work for it.
How true! Of course we all accepted with great enthusiasm. The workshop took
place in Campinas, June 7–11, 2004. It was a wonderful conference, with the
participation of over 100 mathematicians from all over the world.
The wide range of research interests of Djairo is reflected by the articles in this
volume.Throughtheircontributions,theauthorsexpresstheirappreciation,grat-
itude and friendship to Djairo.
We are happy that another eminent Brazilian mathematician, Jacob Palis from
IMPA, has accepted our invitation to give an appreciation of Djairo’s warm per-
sonality and his excelling work.
The editors:
Thierry Cazenave
David Costa
Rau´l Mana´sevich
Orlando Lopes
Paul Rabinowitz
Bernhard Ruf
Carlos Tomei