On the study of semilinear non-local elliptic systems

TL;DR

This paper investigates the existence of solutions for semilinear elliptic systems involving fractional Laplacians, using advanced variational methods and functional analysis to establish new existence results.

Contribution

It introduces novel existence results for fractional Laplacian systems by applying local linking and saddle point theorems, expanding the theoretical understanding of such systems.

Findings

Established new existence results for fractional elliptic systems.

Applied local linking and saddle point theorems effectively.

Provided detailed analysis of the associated function spaces.

Abstract

The purpose of this paper is to study the existence of solutions for semilinear elliptic system driven by fractional Laplacian and establish some new existence results which are obtained by virtue of the local linking theorem and the saddle point theorem. To make the nonlinear scheme feasible, rigorous analysis of the function space involved and corresponding energy functional is necessary.