Evgenios P. Avgerinos, Nikolaos S. Papageorgiou
Topological properties of the solution set of integrodifferential inclusions

Comment.Math.Univ.Carolinae 36,3 (1995) 429-442.

Abstract:In this paper we examine nonlinear integrodifferential inclusions in $\Bbb R^N$. For the nonconvex problem, we show that the solution set is a retract of the Sobolev space $W^{1,1}(T,{\Bbb R^N})$ and the retraction can be chosen to depend continuously on a parameter $\lambda $. Using that result we show that the solution multifunction admits a continuous selector. For the convex problem we show that the solution set is a retract of $C(T,{\Bbb R^N})$. Finally we prove some continuous dependence results.

Keywords: retract, absolute retract, path-connected, Vietoris continuous, $h$-continuous, orientor field
AMS Subject Classification: 34A60

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