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Topological properties of the solution set of integrodifferential inclusions

Evgenios P. Avgerinos, Nikolaos S. Papageorgiou (1995)

Commentationes Mathematicae Universitatis Carolinae

In this paper we examine nonlinear integrodifferential inclusions in N . For the nonconvex problem, we show that the solution set is a retract of the Sobolev space W 1 , 1 ( T , N ) 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 of C ( T , N ) . Finally we prove some continuous dependence results.

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