Geodesic
Topological properties of the solution set of integrodifferential inclusions
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 3, pp. 429-442

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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.
Classification : 34A60, 34K30, 45K05
Keywords: retract; absolute retract; path-connected; Vietoris continuous; $h$-continuous; orientor field 
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     title = {Topological properties of the solution set of integrodifferential inclusions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {429--442},
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Avgerinos, Evgenios P.; Papageorgiou, Nikolaos S. Topological properties of the solution set of integrodifferential inclusions. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 3, pp. 429-442. http://geodesic.mathdoc.fr/item/CMUC_1995__36_3_a3/