Measure of noncompactness on weighted Sobolev space with an application to some nonlinear convolution type integral equations

Abstract

First, we introduce a new measure of noncompactness in weighted Sobolev spaces $$W_{w}^{m,p}(\Omega )$$ , and then as an application, we study the existence of solutions for a class of the nonlinear convolution type integral equations using Darbo’s fixed point theorem associated with this new measure of noncompactness. Further, an example is presented to verify the effectiveness and applicability of our main results.