PORTUGALIAE MATHEMATICA Vol. 58, No. 3, pp. 255270 (2001) 

Topological Properties of Solution Sets for Functional Differential Inclusions Governed by A Family of OperatorsA.G. IbrahimDepartment of Mathematics, Faculty of Science,Cairo University, Giza  EGYPT Abstract: Let $r>0$ be a finite delay and $C([r,t],E)$ be the Banach space of continuous functions from $[r,0]$ to the Banach space $E$. In this paper we prove an existence theorem for functional differential inclusions of the form: $\dot u(t)\in A(t)\,u(t)+F(t,\tau(t)u)$ a.e. on $[0,T]$ and $u=\psi$ on $[r,0]$, where $\{A(t)\dpt t\in [0,T]\}$ is a family of linear operators generating a continuous evolution operator $K(t,s)$, $F$ is a multifunction such that $F(t,\cdot)$ is weakly sequentially hemicontinuous and $\tau(t)\,u(s)=u(t+s)$, for all $t\in [0,T]$ and all $s\in [r,0]$. Also, we are concerned with the topological properties of solution sets. Full text of the article:
Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.
© 2001 Sociedade Portuguesa de Matemática
