Existence and structure of solution sets for impulsive differential inclusions. A survey
type: Item
instance of: scholarly article
zbMATH Open document ID: 1250.34002
author: Smail Djebali
author: Abdelghani Ouahab
author: Lech Górniewicz
publication date: 2012-04-16T00:00:00Z
Mathematics Subject Classification ID: 34-02
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 34K45
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 34K09
zbMATH DE Number: 6024389
zbMATH Keywords: impulsive differential inclusions
zbMATH Keywords: mild solution
zbMATH Keywords: solution set
zbMATH Keywords: topological structure
zbMATH Keywords: semigroup
zbMATH Keywords: fixed point
zbMATH Keywords: Banach space
zbMATH Keywords: half-line
MaRDI profile type: Publication
title: Existence and structure of solution sets for impulsive differential inclusions. A survey
published in: Lecture Notes in Nonlinear Analysis
review text: In this survey paper the authors present some existence results of mild solutions and the topological structure of solutions sets for first order impulsive semilinear differential inclusions with initial and periodic boundary conditions. This survey paper in organized in seven chapters. Chapter one \textit{Introduction} contains, as motivation, some models in which impulsive effects occur. Chapter two \textit{Background material} is devoted to some definitions and preliminary results on multivalued analysis, measure of noncompatness, semigroups and fixed point theorems. In chapter three \textit{Impulsive differential inclusions}, some existence results are presented for impulsive differential inclusions with convex as well as nonconvex valued right hand side. Also the structure of the solution sets is considered. in Chapter four \textit{The periodic problem}, sufficient conditions for the existence of mild solutions for impulsive semilinear differential inclusions with periodic conditions are presented. In Chapter five \textit{Impulsive functional differential inclusions}, the existence of mild solutions and the topological structure for impulsive functional differential inclusions with finite delay are considered. Chapter six \textit{Impulsive differential inclusions on half-time}, is devoted to existence of solutions and the topological structure of the solution sets for impulsive differential inclusions on the half-line. In the last chapter \textit{Concluding remarks} one can find some useful remarks related to the problems considered in the present survey paper. At the end 148 items as references are presented.NEWLINENEWLINEThis survey paper is well written by known specialists in the subject of impulsive differential inclusions, and contains latest progress on the subject. It will be useful for mathematicians, biologists and engineering researchers.
reviewed by: Mouffak Benchohra
description: scientific article; zbMATH DE number 6024389