Multivalued differential equations /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Deimling, Klaus, 1943-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin ; New York : W. de Gruyter, 1992.
Colección:De Gruyter series in nonlinear analysis and applications ; 1.
Temas:
Control theory.
Differential equations, Nonlinear.
Differential inclusions.
Fixed point theory.
Théorie de la commande.
Équations différentielles non linéaires.
Inclusions différentielles.
Théorème du point fixe.
MATHEMATICS > Differential Equations > General.
Control theory
Differential equations, Nonlinear
Differential inclusions
Fixed point theory
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Chapter 1: Multis
  • Â 1 Upper Semicontinuity
  • 1.1 Some Basic Notation
  • 1.2 Upper Semicontinuity
  • 1.3 Properties of Use Multis
  • 1.4 Other Tests for Usc
  • 1.5 Remarks
  • Problems
  • Â 2 Lower Semicontinuity
  • 2.1 Lower Semicontinuity
  • 2.2 Continuous Selections
  • 2.3 Continuity
  • 2.4 Locally Lipschitz Approximations of Usc Multis
  • 2.5 Remarks
  • Problems
  • Â 3 Measurability
  • 3.1 Measurable Multis
  • 3.2 Measurable Selections
  • 3.3 Approximation by Step-Multis
  • 3.4 Some Consequences
  • 3.5 Multis of Two Variables
  • 3.6 RemarksProblems
  • Â 4 Mishmash
  • 4.1 Tangency Conditions
  • 4.2 Bochner Integrals
  • 4.3 Monotone Multis
  • 4.4 Accretive Multis
  • 4.5 Some Basic Facts about Banach Spaces
  • 4.6 Remarks
  • Problems
  • Chapter 2: Existence Theory in Finite Dimensions
  • Â 5 Upper Semicontinuous Right-Hand Sides
  • 5.1 The Usc Case
  • 5.2 Counter-Examples
  • 5.3 The Carathéodory Case
  • 5.4 Some Consequences
  • 5.5 Remarks
  • Problems
  • Â 6 Lower Semicontinuous Right-Hand Sides
  • 6.1 The Lsc Case
  • 6.2 The Carathéodory Case
  • 6.3 Some Consequences
  • 6.4 RemarksProblems
  • Chapter 3: Solution Sets
  • Â 7 Topological Properties of Solution Sets
  • 7.1 Elementary Properties
  • 7.2 Invariance
  • 7.3 Connectedness in the Usc Case
  • 7.4 Connectedness in the Lsc Case
  • 7.5 Funnels
  • 7.6 Remarks
  • Problems
  • Â 8 Comparison of Solutions
  • 8.1 Preliminaries
  • 8.2 Extremal Solutions I
  • 8.3 Extremal Solutions II
  • 8.4 Related Problems
  • 8.5 Gronwallâ€?s Lemma
  • 8.6 Convexification
  • 8.7 Remarks
  • Problems
  • Chapter 4: Existence Theory in Infinite Dimensions
  • Â 9 Compactness Conditions9.1 Two Examples
  • 9.2 Measures of Noncompactness
  • 9.3 The Usc Case
  • 9.4 The Lsc Case
  • 9.5 Remarks
  • Problems
  • Â10 Noncompactness Conditions
  • 10.1 Baire Category
  • 10.2 Extreme Points
  • 10.3 Proof of Theorem 10.1
  • 10.4 Lipschitz Conditions
  • 10.5 Monotonicity
  • 10.6 Hyperaccretivity
  • 10.7 Remarks
  • Problems
  • Chapter 5: Fixed Points and Qualitative Theory
  • Â 11 Fixed Points
  • 11.1 Some (Geo- )metric Results
  • 11.2 Weakly Inward Maps
  • 11.3 Set-Contractions
  • 11.4 Degree Theory
  • 11.5 An Example11.6 Remarks
  • Problems
  • Â 12 Boundary Value Problems
  • 12.1 A Comparison Result
  • 12.2 Sturm/Liouville Problems
  • 12.3 Solutions in Closed Sets
  • 12.4 Remarks
  • Problems
  • Â 13 Periodic Solutions
  • 13.1 Reduction to the Regular Case
  • 13.2 Another Fixed Point Problem
  • 13.3 Examples
  • 13.4 Remarks
  • Problems
  • Â 14 Stability and Asymptotic Behavior
  • 14.1 Stability
  • 14.2 Stability Tests
  • 14.3 Asymptotic Behavior
  • 14.4 Perturbations
  • 14.5 Remarks
  • Problems
  • Appendix: Related Topics

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