Nonlinear quadratic Volterra-Urysohn functional-integral equations in Orlicz spaces

Abstract

The current article discusses the existence of monotonic discontinuous solutions for general nonlinear quadratic Volterra-Urysohn functional-integral equations in Orlicz spaces $E_{\varphi}$ when the function $\varphi$ satisfies the $\Delta_2-$condition.  The case of Lebesgue spaces $L_p$ ($p > 1$) are also examined. We use the arguments of measure of noncompactness with Darbo fixed point theorem to prove our results.