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

TL;DR

This paper investigates the existence of solutions for certain integro-differential systems involving Laplace and bi-Laplace operators, employing fixed point methods and elliptic operator solvability conditions.

Contribution

It establishes the existence of solutions for systems with Laplacian and bi-Laplacian differences using fixed point techniques and elliptic operator theory in unbounded domains.

Findings

Proves existence of solutions under specific conditions.

Utilizes fixed point approach for integro-differential systems.

Addresses solvability without Fredholm property in unbounded domains.

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.