Existence of solutions for some non-Fredholm integro-differential equations with mixed diffusion

Abstract

We establish the existence in the sense of sequences of solutions for certain integro-differential type equations in two dimensions involving the normal diffusion in one direction and the anomalous diffusion in the other direction in H-2(R-2) via the fixed point technique. The elliptic equation contains a second order differential operator without the Fredholm property. It is proved that, under the reasonable technical conditions, the convergence in L-1(R-2) of the integral kernels implies the existence and convergence in H-2(R-2) of the solutions. (C) 2021 Elsevier Inc. All rights reserved.