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Volterra integral inclusions in Banach spaces. (English) Zbl 0659.45010
The author proves the existence of a solution of the integral inclusion \[ x(t)\in p(t)+\int^{t}_{0}K(t,s)F(s,x(s))ds \] in a separable Banach space X under the assumptions that F(t,x) is a compact set in X for each t and x, the function \(x\mapsto F(t,x)\) is Hausdorff continuous, and F satisfies a standard condition concerning the measure of noncompactness. It is stressed that no assumptions involving convexity are involved. Some special kinds of solutions (like extremal solutions and quasitrajectories) are examined as well. Some results concerning weak convergence and a set-valued version of Fatou’s lemma are established.
Reviewer: G.Gripenberg

45N05 Abstract integral equations, integral equations in abstract spaces
45G10 Other nonlinear integral equations
45D05 Volterra integral equations
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