Existence of monotone solutions for a nonlinear quadratic integral equation of Volterra type

In this paper a sufficient condition for the existence of monotone solutions of the following nonlinear quadratic integral equation of Volterra type x(t) = a(t) + g(x(t)) integral(t)(0) v(t, s, x (s))ds, for all t is an element of [0, T], is established. Our approach is based on Darbo's fixed point theorem and the measure of noncompactness introduced by Banal and Olszowy. As applications, some examples to demonstrate our result are given.