Format:
1 online resource (271 pages)
ISBN:
9783110874228
Series Statement:
De Gruyter Series in Nonlinear Analysis and Applications Ser v.1
Content:
The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Please submit book proposals toJürgen Appell.
Content:
Intro -- Chapter 1: Multis -- 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 -- 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 -- 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 Remarks -- Problems -- 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 Remarks -- Problems -- 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 Conditions -- 9.1 Two Examples -- 9.2 Measures of Noncompactness -- 9.3 The Usc Case -- 9.4 The Lsc Case -- 9.5 Remarks -- Problems -- 10 Noncompactness Conditions -- 10.1 Baire Category -- 10.2 Extreme Points.
Note:
Description based on publisher supplied metadata and other sources
Additional Edition:
9783110132120
Additional Edition:
Erscheint auch als Druck-Ausgabe Deimling, Klaus, 1943 - Multivalued differential equations Berlin : de Gruyter, 1992 3110132125
Language:
English
Subjects:
Mathematics
Keywords:
Differentialinklusion
;
Kontrolltheorie
URL:
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