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Approximation of relaxed solutions for lower semicontinuous differential inclusions. (English) Zbl 0755.34015
Let $$F:I\times\mathbb{R}^ n\to\mathbb{R}^ n$$ be a measurable multifunction, with compact values and integrably bounded, such that $$F(t;\bullet)$$ is usc. Define $$G=L^ 1\to L^ 1$$ by $$G(x)=\{v\in L^ 1:v(t)\in F(t,x(t))$$ a.e.}. It is proved that the set of continuous selections from $$G$$ is weakly dense in the set of continuous selections from $$\overline co G$$. Using this result, the author then proves that for any selection $$f\in co F$$, there is a sequence of solutions $$x_ n$$ of $$x\in F(t,x)$$ that converges uniformly to some solution $$x_ *$$ of $$x=f(t,x)$$.
Reviewer: S.Hu (Springfield)

##### MSC:
 34A60 Ordinary differential inclusions 49J45 Methods involving semicontinuity and convergence; relaxation
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