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Keywords:
retract; absolute retract; path-connected; Vietoris continuous; $h$-continuous; orientor field
retract; absolute retract; path-connected; Vietoris continuous; $h$-continuous; orientor field
Summary:
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.
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