Existence Of Solutions For A Class Of Multidimensional Nonlinear Integral Equations

Abstract

In this paper, we construct a measure of noncompactness adapted to multidimensional Lebesgue spaces over product domains. Using this measure together with a Darbo-type fixed point theorem, we prove the existence of at least one solution in Lebesgue spaces for a broad class of multidimensional nonlinear integral equations. This operational framework includes the classical mixed Volterra-Fredholm integral equation as a special case.