Linking Methods in Critical Point Theory

Discusses the problem of finding critical points that are neither maxima nor minima, and presents a systematic way of finding critical points. Based upon the discovery of the fact that there are subsets. DLC: Critical point theory.

Foreword

ix

Preface

xi

Critical Point Theory

1

(20)

Introduction

1

(4)

Other Geometries

5

(2)

Semilinear Boundary Value Problems

7

(2)

The Critical Point Alternative

9

(1)

The Mountain Cliff Theorem

9

(2)

Estimates on Eigenspaces

11

(2)

Asymptotic Limits

13

(1)

Types of Resonance

14

(2)

Multiple Solutions

16

(1)

Eigenvalues

17

(4)

Linking

21

(34)

The Basic Concept

21

(2)

The Flow

23

(4)

Weaker Conditions

27

(3)

Another Form

30

(3)

Some Consequences

33

(3)

Examples of Linking

36

(6)

Critical Sequences

42

(3)

The Compact Case

45

(3)

A Sandwich Theorem

48

(3)

Appendix I: Pseudo-Gradients

51

(1)

Appendix II: Differential Equations

52

(3)

Semilinear Boundary Value Problems

55

(18)

Introduction

55

(3)

Mountain Pass Geometry

58

(4)

Finding a Critical Sequence

62

(1)

Obtaining a Solution

63

(3)

Solving the Problem

66

(2)

Resonance

68

(4)

Appendix I: The Sobolev Inequality

72

(1)

Alternative Methods

73

(26)

Introduction

73

(1)

The Saddle Point Alternative

74

(4)

An Alternate Form

78

(3)

Some Corollaries

81

(4)

An Applications

85

(6)

Superlinear Problems

91

(4)

Some Modifications

95

(4)

Bounded Saddle Point Methods

99

(32)

Introduction

99

(1)

A Bounded Mountain Pass Lemma

100

(5)

The Mountain Pass Alternative

105

(2)

A Compactness Condition

107

(3)

Dual Situations

110

(3)

Combined Results

113

(4)

Nonlinear Eigenvalues

117

(4)

Double Resonance

121

(7)

Appendix I: Generalized Pseudo-Gradients

128

(3)

Estimates on Subspaces

131

(14)

Introduction

131

(1)

Some Important Quantities

132

(5)

The Estimates

137

(3)

Nontrivial Solutions

140

(2)

A Variation

142

(3)

The Fucik Spectrum

145

(22)

Introduction

145

(1)

Jumping Nonlinearities

146

(2)

Quantities Related to the Fucik Spectrum

148

(15)

Applications

163

(4)

Resonance

167

(38)

Introduction

167

(1)

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Linking Methods in Critical Point Theory

Summary

Table of Contents

Supplemental Materials