Existence and uniqueness of solution for a nonhomogeneous nonlocal problem

TL;DR

This paper studies a class of elliptic problems with nonlocal Kirchhoff operators, establishing conditions for the existence and uniqueness of solutions despite variable coefficients and sign-changing data.

Contribution

It provides new conditions ensuring existence and uniqueness for nonlocal Kirchhoff problems with sign-changing data and variable coefficients.

Findings

Proved existence of solutions under certain conditions.

Established uniqueness of solutions.

Handled sign-changing data in nonlocal elliptic problems.

Abstract

In this paper we investigate a class of elliptic problems involving a nonlocal Kirchhoff type operator with variable coefficients and data changing its sign. Under appropriated conditions on the coefficients, we have shown existence and uniqueness of solution.