Existence of solutions for implicit functional-integral equations associated with discontinuous functions

Let I := [0, 1]. In this paper we deal with the functional-integral equation h(u(t)) = g(t) + f(t, integral(I) k(t, s) u(phi(s))ds) for a.c. t is an element of I. While in most literature the function f is usually requested to be a Caratheodory map, we prove an existence result for solutions u is an element of L-p(I) (with p is an element of]1, +infinity]), where the continuity of f with respect to the second variable is not assumed. As a matter of fact, a function f satisfying the assumptions of our result can be discontinuous, with respect to the second variable, even at each point of its domain.