In this paper we investigate the existence of mild solutions to second order initial value problems for a class of delay integrodifferential inclusions with nonlocal conditions. We rely on a fixed point theorem for condensing maps due to Martelli.
The nonimprovable sufficient conditions for the unique solvability of the problem u' (t) = l(u)(t) + q(t), u(a) = c, where l : C(I; R) → L(I; R) is a linear bounded operator, q ∈ L(I; R), c ∈ R, are established which are different from the previous results. More precisely, they are interesting especially in the case where the operator ` is not of Volterra’s type with respect to the point a.