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Existence and Topological Properties of Solution Sets for Differential Inclusions with Delay

Gomaa A,M

Commentationes Mathematicae

2008

Vol. 48, [Z] 1

45-58

We consider the problem [formula] in a Banach space E, where belongs to the Banach space, CE([-d, 0]), of all continuous functions from [-d, 0] into E. A multifunction F from [0, b] × CE([-d, 0]) into the set, Pfc(E), of all nonempty closed convex subsets of E is weakly sequentially hemi-continuous, tx(s) = x(t + s) for all s 2 [-d, 0] and {A(t) : 0 6 t 6 b} is a family of densely defined closed linear operators generating a continuous evolution operator S(t, s). Under a generalization of the compactness assumptions, we prove an existence result and give some topological properties of our solution sets that generalizes earlier theorems by Papageorgiou, Rolewicz, Deimling, Frankowska and Cichon..

On theorems for weak solutions of nonlinear differential equations with and without delay in Banach spaces

Gomaa A,M

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2007

Vol. 47, [Z] 2

179-191

In the present work we give an existence theorem for bounded weak solution of the differential equation.......[formuła matematyczna]