Volterra integral inclusions in Banach spaces
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.
scientific article; zbMATH DE number 4077979