Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces.

Intro -- Introduction -- 1 Multivalued maps: general properties -- 1.1 Continuity of multimaps -- 1.2 Operations on multimaps. Selections and approximations -- 1.3 Measurable multimaps and the superposition multioperator -- Bibliographic notes -- 2 Measures of noncompactness and condensing multimaps -- 2.1 Measures of noncompactness -- 2.2 Condensing multimaps -- Bibliographic notes -- 3 Topological degree theory for condensing multifields -- 3.1 The relative topological degree and fixed points of compact multimaps -- 3.2 Topological degree for condensing multifields -- 3.3 The evaluation of the degree -- 3.4 The topological degree for condensing nonconvex-valued multimaps -- 3.5 Some properties of the fixed points set -- 3.6 Solvability of systems of inclusions with condensing multioperators -- Bibliographic notes -- 4 Semigroups and measures of noncompactness -- 4.1 Semigroups: general facts -- 4.2 Measures of noncompactness in function spaces: measurability and integrability -- 4.3 Condensing semigroups -- Bibliographic notes -- 5 Semilinear differential inclusions: initial problem -- 5.1 Integral multioperator -- 5.2 Existence and continuous dependence theorems -- 5.3 The structure of the solutions set -- 5.4 The averaging principle -- 5.5 On inclusions with almost lower semicontinuous nonlinearities -- Bibliographic notes -- 6 Semilinear inclusions: periodic problems -- 6.1 The integral multioperator for a periodic problem -- 6.2 The averaging principle for a periodic problem -- 6.3 The translation multioperator -- Bibliographic notes -- Bibliography -- Index.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.