Multivalued Differential Equations ( De Gruyter Series in Nonlinear Analysis and Applications )

Publication series :De Gruyter Series in Nonlinear Analysis and Applications

Author: Klaus Deimling  

Publisher: De Gruyter‎

Publication year: 1992

E-ISBN: 9783110874228

P-ISBN(Paperback): 9783110132120

Subject: O175.1 Ordinary Differential Equations

Language: ENG

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Chapter

Chapter 1: Multis

pp.:  1 – 13

§ 1 Upper Semicontinuity

pp.:  13 – 15

1.2 Upper Semicontinuity

pp.:  15 – 16

1.1 Some Basic Notation

pp.:  15 – 15

1.3 Properties of Use Multis

pp.:  16 – 18

1.4 Other Tests for Usc

pp.:  18 – 20

1.5 Remarks

pp.:  20 – 20

Problems

pp.:  20 – 21

§ 2 Lower Semicontinuity

pp.:  21 – 24

2.1 Lower Semicontinuity

pp.:  24 – 24

2.2 Continuous Selections

pp.:  24 – 25

2.3 Continuity

pp.:  25 – 27

2.5 Remarks

pp.:  28 – 29

Problems

pp.:  29 – 30

§ 3 Measurability

pp.:  30 – 33

3.1 Measurable Multis

pp.:  33 – 33

3.2 Measurable Selections

pp.:  33 – 34

3.3 Approximation by Step-Multis

pp.:  34 – 35

3.4 Some Consequences

pp.:  35 – 37

3.5 Multis of Two Variables

pp.:  37 – 38

3.6 Remarks

pp.:  38 – 39

Problems

pp.:  39 – 40

§ 4 Mishmash

pp.:  40 – 43

4.1 Tangency Conditions

pp.:  43 – 43

4.2 Bochner Integrals

pp.:  43 – 46

4.3 Monotone Multis

pp.:  46 – 47

4.4 Accretive Multis

pp.:  47 – 50

4.5 Some Basic Facts about Banach Spaces

pp.:  50 – 54

4.6 Remarks

pp.:  54 – 55

Problems

pp.:  55 – 56

Chapter 2: Existence Theory in Finite Dimensions

pp.:  56 – 61

§ 5 Upper Semicontinuous Right-Hand Sides

pp.:  61 – 64

5.1 The Usc Case

pp.:  64 – 65

5.2 Counter-Examples

pp.:  65 – 66

5.3 The Carathéodory Case

pp.:  66 – 68

5.4 Some Consequences

pp.:  68 – 70

5.5 Remarks

pp.:  70 – 72

Problems

pp.:  72 – 73

§ 6 Lower Semicontinuous Right-Hand Sides

pp.:  73 – 77

6.1 The Lsc Case

pp.:  77 – 78

6.2 The Carathéodory Case

pp.:  78 – 80

6.3 Some Consequences

pp.:  80 – 83

6.4 Remarks

pp.:  83 – 86

Problems

pp.:  86 – 87

Chapter 3: Solution Sets

pp.:  87 – 89

§ 7 Topological Properties of Solution Sets

pp.:  89 – 91

7.2 Invariance

pp.:  91 – 92

7.1 Elementary Properties

pp.:  91 – 91

7.3 Connectedness in the Usc Case

pp.:  92 – 93

7.4 Connectedness in the Lsc Case

pp.:  93 – 96

7.6 Remarks

pp.:  96 – 97

7.5 Funnels

pp.:  96 – 96

Problems

pp.:  97 – 99

§ 8 Comparison of Solutions

pp.:  99 – 103

8.2 Extremal Solutions I

pp.:  103 – 104

8.1 Preliminaries

pp.:  103 – 103

8.3 Extremal Solutions II

pp.:  104 – 107

8.4 Related Problems

pp.:  107 – 110

8.5 Gronwall’s Lemma

pp.:  110 – 112

8.6 Convexification

pp.:  112 – 114

8.7 Remarks

pp.:  114 – 117

Problems

pp.:  117 – 117

Chapter 4: Existence Theory in Infinite Dimensions

pp.:  117 – 121

§ 9 Compactness Conditions

pp.:  121 – 123

9.2 Measures of Noncompactness

pp.:  123 – 125

9.1 Two Examples

pp.:  123 – 123

9.3 The Usc Case

pp.:  125 – 127

9.4 The Lsc Case

pp.:  127 – 131

9.5 Remarks

pp.:  131 – 136

Problems

pp.:  136 – 137

§10 Noncompactness Conditions

pp.:  137 – 142

10.2 Extreme Points

pp.:  142 – 143

10.1 Baire Category

pp.:  142 – 142

10.3 Proof of Theorem 10.1

pp.:  143 – 145

10.4 Lipschitz Conditions

pp.:  145 – 147

10.5 Monotonicity

pp.:  147 – 148

10.6 Hyperaccretivity

pp.:  148 – 152

10.7 Remarks

pp.:  152 – 153

Problems

pp.:  153 – 154

Chapter 5: Fixed Points and Qualitative Theory

pp.:  154 – 155

§ 11 Fixed Points

pp.:  155 – 158

11.2 Weakly Inward Maps

pp.:  158 – 161

11.1 Some (Geo-)metric Results

pp.:  158 – 158

11.3 Set-Contractions

pp.:  161 – 163

11.4 Degree Theory

pp.:  163 – 166

11.5 An Example

pp.:  166 – 168

11.6 Remarks

pp.:  168 – 170

Problems

pp.:  170 – 172

§ 12 Boundary Value Problems

pp.:  172 – 176

12.2 Sturm/Liouville Problems

pp.:  176 – 179

12.1 A Comparison Result

pp.:  176 – 176

12.3 Solutions in Closed Sets

pp.:  179 – 185

12.4 Remarks

pp.:  185 – 189

Problems

pp.:  189 – 190

§ 13 Periodic Solutions

pp.:  190 – 193

13.1 Reduction to the Regular Case

pp.:  193 – 193

13.2 Another Fixed Point Problem

pp.:  193 – 194

13.3 Examples

pp.:  194 – 198

13.4 Remarks

pp.:  198 – 209

Problems

pp.:  209 – 209

§ 14 Stability and Asymptotic Behavior

pp.:  209 – 214

14.1 Stability

pp.:  214 – 214

14.2 Stability Tests

pp.:  214 – 216

14.3 Asymptotic Behavior

pp.:  216 – 220

14.4 Perturbations

pp.:  220 – 225

14.5 Remarks

pp.:  225 – 229

Problems

pp.:  229 – 234

Appendix: Related Topics

pp.:  234 – 239

A 1. Discontinuous Differential Equations

pp.:  239 – 239

A 2. Implicit Differential Equations

pp.:  239 – 245

A 3. Functional Differential Equations

pp.:  245 – 247

A 4. Perturbations of Dissipative Right-Hand Sides

pp.:  247 – 249

References

pp.:  249 – 255

Index

pp.:  255 – 271

LastPages

pp.:  271 – 273

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