Solvability of a class of integro-differential equations with Laplace and bi-Laplace operators

TL;DR

This paper investigates the existence of solutions for a class of integro-differential equations involving Laplace and bi-Laplace operators, using fixed point methods and solvability conditions for non-Fredholm elliptic operators.

Contribution

It introduces new solvability results for integro-differential equations with Laplacian and bi-Laplacian terms in unbounded domains, employing fixed point techniques.

Findings

Established existence of solutions under specific conditions.

Applied solvability conditions for non-Fredholm elliptic operators.

Extended analysis to unbounded domains.

Abstract

The work deals with the studies of the existence of solutions of an integro-differential equation in the situation of the difference of the standard Laplacian and the bi-Laplacian in the diffusion term. The proof of the existence of solutions relies on a fixed point technique. We use the solvability conditions for the non-Fredholm elliptic operators in unbounded domains.