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E-BOOK
Title Multivalued differential equations / Klaus Deimling.
Imprint Berlin ; New York : W. de Gruyter, 1992.

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 Internet  Electronic Book    AVAILABLE
Description 1 online resource (xi, 260 pages) : illustrations
Series De Gruyter series in nonlinear analysis and applications ; 1
De Gruyter series in nonlinear analysis and applications ; 1.
Bibliog. Includes bibliographical references and index.
Note Available only to authorized UTEP users.
English.
Subject Control theory.
Differential equations, Nonlinear.
Differential inclusions.
Fixed point theory.
Contents 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 --  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 --  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 --  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 --  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 --  8 Comparison of Solutions -- 8.1 Preliminaries -- 8.2 Extremal Solutions I -- 8.3 Extremal Solutions II -- 8.4 Related Problems -- 8.5 Gronwall�s Lemma -- 8.6 Convexification -- 8.7 Remarks -- Problems -- Chapter 4: Existence Theory in Infinite Dimensions
 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 --  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
Other Title Print version: Deimling, Klaus, 1943- Multivalued differential equations. Berlin ; New York : W. de Gruyter, 1992