Nonlinear Analysis

List of Contributors

Preface

Periodic Solutions of Semilinear Parabolic Equations

Introduction 1


1. Definitions and Main Results


2. Preliminaries on Linear Evolution Equations


3. Semilinear Evolution Equations


4. Semilinear Parabolic Equations


5. Proof of the Main Results

References

Linear Maximal Monotone Operators and Singular Nonlinear Integral Equations of Hammerstein Type

Introduction


1. Proof of the Main Theorem


2. Application to Hammerstein Equations

References

Nonlinear Problems Across a Point of Resonance for Non-Self-Adjoint Systems


1. Introduction


2. Notations


3. Some Abstract Existence Theorems


4. A Study on in the Uniform Topology


5. Existence Theorems for the Scalar Case by Uniform Topology


6. Extensions to the Case of P and Q Orthogonal

References

Branching of Periodic Solutions of Nonautonomous Systems

Introduction


1. Existence of Periodic Solutions


2. Stability of Periodic Solutions

References

Restricted Generic Bifurcation

Introduction


1. Motivation and Statement of the Problems


2. Restricted Generic Bifurcation, p = 1


3. Restricted Generic Bifurcation, p = 2

References

On a Second-Order Nonlinear Elliptic Boundary Value Problem


1. Introduction and Statement of the Result


2. Proof of the Theorem

References

Tikhonov Regularization and Nonlinear Problems at Resonance—Deterministic and Random


1. Introduction


2. Linear Case


3. Alternative Method


4. Perturbation Method


5. The Proximal Point Algorithm


6. Existence of Random Solutions


7. Tikhonov Regularization and Random Problems

References

The Eigenvalue Problem for Variational Inequalities and a New Version of the Ljustemik-Schnirelmann Theory

Introduction: Motivation


1. A Simple Example


2. General Theory. The Penalty Method and a New Version

of the Ljustemik-Schnirelmann Theory


3. Special Case of a Halfspace


4. An Open Problem

References

Nonlinear Boundary Value Problems for Ordinary Differential Equations: From Schauder Theorem to Stable Homotopy


1. Introduction


2. Formulation of the Problem


3. The Case Where L Has an Inverse


4. The Case of Linear Boundary Conditions Such That L Has No Inverse


5. The Case of Nonlinear Boundary Conditions Such That Ind L = 0

References

Some Minimax Theorems and Applications to Nonlinear Partial Differential Equations

Introduction


1. The Abstract Theorems


2. Applications to Elliptic Partial Differential Equations


3. An Application to a Hyperbolic Partial

Differential Equation

References

Branching and Stability for Nonlinear Gradient Operators


1. Introduction


2. Preliminaries


3. The Branching Theorems for Equation (*)


4. The Stability Results

References

Recent Progress in Bifurcation Theory


1. Bifurcation Theory


2. Bifurcation at Multiple Eigenvalues


3. Bifurcation in the Presence of a Symmetry Group


4. Bifurcation of Doubly Periodic Solutions

References

On the Subgradient of Convex Functionals


1. BBeДeHиe


2. OcHOBHъie ПOЯЯTя и BcпomraTeлbHbie ПpeДлoЖeHИЯ


3. ДOKa3aTeЛbCTBO TeopembI 4

ЛИTepaTypa

On the Stability of Bifurcating Solutions


1. Introduction


2. The Steady-State Bifurcation

References

Published Works of Erich H. Rothe