Saddle point solutions for non-local elliptic operators

TL;DR

This paper investigates solutions to non-local elliptic equations with variational structure, employing saddle point methods to establish existence results for equations involving integrodifferential operators with Dirichlet boundary conditions.

Contribution

It introduces a novel application of the Saddle Point Theorem to non-local elliptic equations driven by integrodifferential operators, expanding the analytical toolkit for such problems.

Findings

Existence of solutions established using saddle point methods

Application of variational techniques to non-local operators

Framework applicable to a class of integrodifferential equations

Abstract

The paper deals with equations driven by a non-local integrodifferential operator $\mathcal L_K$ with homogeneous Dirichlet boundary conditions. These equations have a variational structure and we find a solution for them using the Saddle Point Theorem.