Multivalued Differential Equations
eBook - PDF

Multivalued Differential Equations

  1. 271 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Multivalued Differential Equations

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Information

Publisher
De Gruyter
Year
2011
Print ISBN
9783110132120
eBook ISBN
9783110874228
Edition
1
Topic
Mathematics
Subtopic
Mathematical Analysis
Index
Mathematics

Table of contents

  1. Chapter 1: Multis
  2. § 1 Upper Semicontinuity
  3. 1.1 Some Basic Notation
  4. 1.2 Upper Semicontinuity
  5. 1.3 Properties of Use Multis
  6. 1.4 Other Tests for Usc
  7. 1.5 Remarks
  8. Problems
  9. § 2 Lower Semicontinuity
  10. 2.1 Lower Semicontinuity
  11. 2.2 Continuous Selections
  12. 2.3 Continuity
  13. 2.4 Locally Lipschitz Approximations of Usc Multis
  14. 2.5 Remarks
  15. Problems
  16. § 3 Measurability
  17. 3.1 Measurable Multis
  18. 3.2 Measurable Selections
  19. 3.3 Approximation by Step-Multis
  20. 3.4 Some Consequences
  21. 3.5 Multis of Two Variables
  22. 3.6 Remarks
  23. Problems
  24. § 4 Mishmash
  25. 4.1 Tangency Conditions
  26. 4.2 Bochner Integrals
  27. 4.3 Monotone Multis
  28. 4.4 Accretive Multis
  29. 4.5 Some Basic Facts about Banach Spaces
  30. 4.6 Remarks
  31. Problems
  32. Chapter 2: Existence Theory in Finite Dimensions
  33. § 5 Upper Semicontinuous Right-Hand Sides
  34. 5.1 The Usc Case
  35. 5.2 Counter-Examples
  36. 5.3 The Carathéodory Case
  37. 5.4 Some Consequences
  38. 5.5 Remarks
  39. Problems
  40. § 6 Lower Semicontinuous Right-Hand Sides
  41. 6.1 The Lsc Case
  42. 6.2 The Carathéodory Case
  43. 6.3 Some Consequences
  44. 6.4 Remarks
  45. Problems
  46. Chapter 3: Solution Sets
  47. § 7 Topological Properties of Solution Sets
  48. 7.1 Elementary Properties
  49. 7.2 Invariance
  50. 7.3 Connectedness in the Usc Case
  51. 7.4 Connectedness in the Lsc Case
  52. 7.5 Funnels
  53. 7.6 Remarks
  54. Problems
  55. § 8 Comparison of Solutions
  56. 8.1 Preliminaries
  57. 8.2 Extremal Solutions I
  58. 8.3 Extremal Solutions II
  59. 8.4 Related Problems
  60. 8.5 Gronwall’s Lemma
  61. 8.6 Convexification
  62. 8.7 Remarks
  63. Problems
  64. Chapter 4: Existence Theory in Infinite Dimensions
  65. § 9 Compactness Conditions
  66. 9.1 Two Examples
  67. 9.2 Measures of Noncompactness
  68. 9.3 The Usc Case
  69. 9.4 The Lsc Case
  70. 9.5 Remarks
  71. Problems
  72. §10 Noncompactness Conditions
  73. 10.1 Baire Category
  74. 10.2 Extreme Points
  75. 10.3 Proof of Theorem 10.1
  76. 10.4 Lipschitz Conditions
  77. 10.5 Monotonicity
  78. 10.6 Hyperaccretivity
  79. 10.7 Remarks
  80. Problems
  81. Chapter 5: Fixed Points and Qualitative Theory
  82. § 11 Fixed Points
  83. 11.1 Some (Geo-)metric Results
  84. 11.2 Weakly Inward Maps
  85. 11.3 Set-Contractions
  86. 11.4 Degree Theory
  87. 11.5 An Example
  88. 11.6 Remarks
  89. Problems
  90. § 12 Boundary Value Problems
  91. 12.1 A Comparison Result
  92. 12.2 Sturm/Liouville Problems
  93. 12.3 Solutions in Closed Sets
  94. 12.4 Remarks
  95. Problems
  96. § 13 Periodic Solutions
  97. 13.1 Reduction to the Regular Case
  98. 13.2 Another Fixed Point Problem
  99. 13.3 Examples
  100. 13.4 Remarks
  101. Problems
  102. § 14 Stability and Asymptotic Behavior
  103. 14.1 Stability
  104. 14.2 Stability Tests
  105. 14.3 Asymptotic Behavior
  106. 14.4 Perturbations
  107. 14.5 Remarks
  108. Problems
  109. Appendix: Related Topics
  110. A 1. Discontinuous Differential Equations
  111. A 2. Implicit Differential Equations
  112. A 3. Functional Differential Equations
  113. A 4. Perturbations of Dissipative Right-Hand Sides
  114. References
  115. Index

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