Existence and convergence results for integral inclusions in Banach spaces (Q1118123)

The author proves the existence of a solution of the multivalued Volterra integral equation \[ x(t)\in p(t)+\int^{t}_{0}K(t,s)F(s,x(s))ds \] in a separable Banach space X under the assumptions that F(t,x) is a contained in a weakly compact set in X for each t and x, and K satisfies a standard continuity condition. The continuity assumptions on F depend on whether F(t,x) is convex or nonconvex. A result on the continuous dependence of solutions is given. Some more general results on multifunctions are also presented. The same equation is also studied by the author [ibid. 1, 65-81 (1988; Zbl 0659.45010)].