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On multivalued evolution equations and differential inclusions in Banach spaces. (English) Zbl 0641.47052
The author studies the nonemptyness and the topological structure of the set of mild solutions of the Cauchy problem: $$x'(t)\in (A(t)x(t)+F(t,x(t))$$, $$0\leq t\leq b$$; $$x(0)=x_ 0$$, where $$\{$$ A(t);0$$\leq t\leq b\}$$ is a family of closed, linear operators in a separable Banach space X and F($$\cdot,\cdot)$$ is a multifunction from [0,b]$$\times X$$ into X. He proves the existence of mild solutions and the fact that the set of mild solutions is an $$R_{\delta}$$-set, i.e. it is homeomorphic to the intersection of a decreasing sequence of compact absolute retracts.
Reviewer: Gh.Moroşanu

##### MSC:
 47E05 General theory of ordinary differential operators 34A60 Ordinary differential inclusions 47H20 Semigroups of nonlinear operators