A family of measures of noncompactness in the space Lploc(ℝN) and its application to some nonlinear convolution type integral equations

Abstract

Abstract The aim of the present paper is to introduce a new family of measures of noncompactness on the Fréchet space LPloc(ℝN) (1 ≤ p < ∞). Further, we prove a fixed point theorem on the family of measures of noncompactness in LPloc(ℝN). As an application, we investigate the existence of entire solutions for some classes of nonlinear functional integral equations of convolution type associated with the new family of measures of noncompactness. Finally, we give an illustrative example to verify the effectiveness and applicability of our results.