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Topological properties of the solution set of integrodierential inclusions

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Evgenios P. Avgerinos, Nikolaos S. Papageorgiou

Topological properties of the solution set of integrodierential inclusions

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

Abstract: In this paper we examine nonlinear integrodifferential inclusions inRN. For the nonconvex problem, we show that the solution set is a retract of the Sobolev spaceW1,1(T,RN) and the retraction can be chosen to depend continuously on a parameter λ. 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 ofC(T,RN). 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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