Nonlinear analysis and differential equations

✍ Scribed by M.R. Grossinho, M. Ramos, C. Rebelo, L. Sanchez

• Publisher: Birkhäuser Boston
• Year: 2000
• Tongue: English
• Leaves: 400
• Series: Progress in Nonlinear Differential Equations and Their Applications
• Edition: 1
• Category: Library

✦ Synopsis

This work, consisting of expository articles as well as research papers, highlights recent developments in nonlinear analysis and differential equations. The material is largely an outgrowth of autumn school courses and seminars held at the University of Lisbon and has been thoroughly refereed.

Several topics in ordinary differential equations and partial differential equations are the focus of key articles, including:

periodic solutions of systems with p-Laplacian type operators (J. Mawhin)

bifurcation in variational inequalities (K. Schmitt)

a geometric approach to dynamical systems in the plane via twist theorems (R. Ortega)

asymptotic behavior and periodic solutions for Navier--Stokes equations (E. Feireisl)

mechanics on Riemannian manifolds (W. Oliva)

techniques of lower and upper solutions for ODEs (C. De Coster and P. Habets)

A number of related subjects dealing with properties of solutions, e.g., bifurcations, symmetries, nonlinear oscillations, are treated in other articles.

This volume reflects rich and varied fields of research and will be a useful resource for mathematicians and graduate students in the ODE and PDE community.

✦ Table of Contents

Front Cover......Page 1
Title......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 10
List of Participants......Page 12
Part 1. Short courses......Page 16
An Overview of the Method of Lower and Upper Solutions for ODES ......Page 18
On the Long-time Behaviour of Solutions to the Navier-Stokes Equations of Compressible Flow ......Page 39
Periodic Solutions of Systems with p-Laplacian-like Operators ......Page 52
Mechanics on Riemannian Manifolds ......Page 80
Twist Mappings, Invariant Curves and Periodic Differential Equations ......Page 100
Variational Inequalities, Bifurcation and Applications ......Page 128
Part 2. Seminar papers ......Page 160
Complex Dynamics in a Class of Reversible Equations ......Page 162
Symmetry and Monotonicity Results for Solutions of Certain Elliptic PDEs on Manifolds ......Page 176
Nielsen Number and Multiplicity Results for Multivalued Boundary Value Problems ......Page 190
Bifurcation Theory and Application to Semilinear Problems near the Resonance Parameter ......Page 204
Orientation and Degree for Fredholm Maps of Index Zero Between Banach Spaces ......Page 216
On the Method of Upper and Lower Solutions for First Order BVPs ......Page 230
Nonlinear Optimal Control Problems for Diffusive Elliptic Equations of Logistic Type ......Page 236
On The Use of Time-Maps in Nonlinear Boundary Value Problems ......Page 246
Some Aspects of Nonlinear Spectral Theory ......Page 258
Asymmetric Nonlinear Oscillators ......Page 268
Hopf Bifurcation for a Delayed Predator-Prey Model and the Effect of Diffusion ......Page 272
Galerkin-Averaging Method in Infinite-Dimensional Spaces for Weakly Nonlinear Problems ......Page 284
PBVPs for Ordinary Impulsive Differential Equations ......Page 296
Homoclinic and Periodic Solutions for Some Classes of Second Order Differential Equations.......Page 304
Global Bifurcation for Monge-Ampere Operators ......Page 314
Remarks on Boundedness of Semilinear Oscillators ......Page 326
The Dual Variational Method in Nonlocal Semilinear Tricomi Problems ......Page 336
Symmetry Properties of Positive Solutions of Nonlinear Differential Equations Involving the p-Laplace Operator ......Page 354
A Maximum Principle with Applications to the Forced Sine-Gordon Equation ......Page 362
Lipschitzian Regularity Conditions for the Minimizing Trajectories of Optimal Control Problems ......Page 372
Abstract Concentration Compactness and Elliptic Equations on Unbounded Domains ......Page 384