This monograph is devoted to the development of a unified approach for studying differential inclusions in a Banach space with non-convex right-hand side, a new branch of the classical theory of ordinary differential equations. Differential inclusions are now a mature field of mathematical activity, with their own methods, techniques, and applications, which range from economics to physics and biology. The current approach relies on ideas and methods from modern functional analysis, general topology, the theory of multifunctions, and continuous selectors.
Audience: This volume will be of interest to researchers and postgraduate student whose work involves differential equations, functional analysis, topology, and the theory of set-valued functions.
Table of ContentsPreface. 1. Multi-Valued Differential Equation Generated by a Differential Inclusion. 2. Differential Inclusions. Existence of Solutions. 3. Properties of Solutions. 4. Integral Funnel of the Differential Inclusion. 5. Inclusions with Non-Compact Right Hand Side. Appendices. References. Index. Symbols.