This volume represents a broad survey of current research in the fields of nonlinear analysis and nonlinear differential equations. It is dedicated to Djairo G. de Figueiredo on the occasion of his 70th birthday. The collection of 34 research and survey articles reflects the wide range of interests of Djairo de Figueiredo, including:
- various types of nonlinear partial differential equations and systems, in particular equations of elliptic, parabolic, hyperbolic and mixed type;
- equations of Schrödinger, Maxwell, Navier-Stokes, Bernoulli-Euler, Seiberg-Witten, Caffarelli-Kohn-Nirenberg;
- existence, uniqueness and multiplicity of solutions;
- critical Sobolev growth and connected phenomena;
- qualitative properties, regularity and shape of solutions;
- inequalities, a-priori estimates and asymptotic behavior;
- various applications to models such as asymptotic membranes, nonlinear plates and inhomogeneous fluids.
The contributions of so many distinguished mathematicians to this volume document the importance and lasting influence of the mathematical research of Djairo de Figueiredo. The book thus is a source of new ideas and results and should appeal to graduate students and mathematicians interested in nonlinear problems.
Author(s): Emerson A. M. Abreu, Paulo Cesar Carrião (auth.), Thierry Cazenave, David Costa, Orlando Lopes, Raúl Manásevich, Paul Rabinowitz, Bernhard Ruf, Carlos Tomei (eds.)
Series: Progress in Nonlinear Differential Equations and Their Applications 66
Edition: 1
Publisher: Birkhäuser Basel
Year: 2006
Language: English
Pages: 520
City: Basel; Boston
Tags: Partial Differential Equations; Analysis
Remarks on a Class of Neumann Problems Involving Critical Exponents....Pages 1-15
Existence of Solutions for a Class of Problems in IR N Involving the p ( x )-Laplacian....Pages 17-32
A Unitarian Approach to Classical Electrodynamics: The Semilinear Maxwell Equations....Pages 33-52
Existence of Solutions for the Nonlinear Schrödinger Equation with V (∞) = 0....Pages 53-65
Asymptotic Behavior of a Bernoulli-Euler Type Equation with Nonlinear Localized Damping....Pages 67-91
T-minima....Pages 93-103
A Note on Heteroclinic Solutions of Mountain Pass Type for a Class of Nonlinear Elliptic PDE’s....Pages 105-114
Existence of Multiple Solutions for Quasilinear Equations via Fibering Method....Pages 115-134
Symmetry of Solutions of a Semilinear Elliptic Problem in an Annulus....Pages 135-147
Construction of a Radial Solution to a Superlinear Dirichlet Problem that Changes Sign Exactly Once....Pages 149-160
Global Solvability and Asymptotic Stability for the Wave Equation with Nonlinear Boundary Damping and Source Term....Pages 161-184
Positive Solutions for a Class of Nonlocal Elliptic Problems....Pages 185-194
On a Class of Critical Elliptic Equations of Caffarelli-Kohn-Nirenberg Type....Pages 195-206
Existence and Number of Solutions for a Class of Semilinear Schrödinger Equations....Pages 207-220
Multiparameter Elliptic Equations in Annular Domains....Pages 221-231
Variational Principle for the Seiberg-Witten Equations....Pages 233-245
Some Recent Results on Equations Involving the Pucci’s Extremal Operators....Pages 247-261
Principal Eigenvalue in an Unbounded Domain and a Weighted Poincaré Inequality....Pages 263-281
Uniform Stabilization for a Hyperbolic Equation with Acoustic Boundary Conditions in Simple Connected Domains....Pages 283-296
Some Remarks on Semilinear Resonant Elliptic Problems....Pages 297-312
Remarks on Regularity Theorems for Solutions to Elliptic Equations via the Ultracontractivity of the Heat Semigroup....Pages 313-320
2d Ladyzhenskaya-Solonnikov Problem for Inhomogeneous Fluids....Pages 321-350
Generalization of a Well-known Inequality....Pages 351-364
Nonexistence of Nontrivial Solutions for Supercritical Equations of Mixed Elliptic-Hyperbolic Type....Pages 365-370
On the Shape of Least-Energy Solutions to a Quasilinear Elliptic Equation Involving Critical Sobolev Exponents....Pages 371-390
A-priori Bounds and Positive Solutions to a Class of Quasilinear Elliptic Equations....Pages 391-406
The Role of the Equal-Area Condition in Internal and Superficial Layered Solutions to Some Nonlinear Boundary Value Elliptic Problems....Pages 407-413
Some Recent Results Regarding Symmetry and Symmetry-breaking Properties of Optimal Composite Membranes....Pages 415-427
Generic Simplicity for the Solutions of a Nonlinear Plate Equation....Pages 429-442
An Estimate for the Blow-up Time in Terms of the Initial Data....Pages 443-463
Lorentz Spaces and Nonlinear Elliptic Systems....Pages 465-469
The Topology of Critical Sets of Some Ordinary Differential Operators....Pages 471-489
A Note on the Superlinear Ambrosetti-Prodi Type Problem in a Ball....Pages 491-504
....Pages 505-518
