Existence of stationary solutions for some systems of integro-differential equations with Laplace and bi-Laplace operators

Abstract

The article is devoted to the solvability of a system of integro-differential equations in the case of the difference of the standard Laplacian and the bi-Laplacian in the diffusion terms. The proof of the existence of solutions is based on a fixed point technique. We use the solvability conditions for the elliptic operators without the Fredholm property in unbounded domains.