Contents
Dedication. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
J. Palis
On Djairo de Figueiredo. A Mathematician . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xi
E.A.M. Abreu, P.C. Carri˜ao 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 Schr¨odinger Equation
with V (∞) = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
R.C. Char˜ao, 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-Nirenberg Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Y. Ding and A. Szulkin
Existence and Number of Solutions for a Class of Semilinear
Schr¨odinger 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´e Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .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–Solonnikov Problem 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