Condensing multivalued maps and semilinear differential inclusions in Banach spaces (Q2715760)

The book is devoted to some aspects of multivalued analysis. It is organized into six chapters. Chapter 1 recalls general definitions and properties of multivalued maps and focuses special attention to measurable multimaps and to the superposition multioperator. Chapter 2 describes the main results of the theory of measures of noncompactness in Banach spaces and specifies the notion of condensing multimap relative to a measure of noncompactness. Chapter 3 investigates the topological degree for different types of condensing multifields in Banach spaces. A study of the existence of solutions to a system of inclusions with condensing multioperators is developed and applied to obtain optimal control for systems governed by a neutral functional-differential equation. Chapter 4 summarizes some results dealing with strongly continuous semigroups that are necessary to the study of semilinear inclusions. This is done in the last two chapters. Chapter 5 presents results concerning the existence of local and global solutions, the topological structure of the solution set and the dependence of the solutions on parameters and initial data. In Chapter 6, the authors develop methods for justifying the averaging principle in periodic problems and for proving the existence of a periodic solution and the existence of a global attractor of semilinear differential inclusions satisfying a dissipativity condition. NEWLINENEWLINENEWLINEThe presentation is self-contained, and the subject is addressed to graduate students as well as to researchers in applied functional analysis.