On strongly indefinite systems involving the fractional Laplacian

TL;DR

This paper investigates strongly indefinite systems with the fractional Laplacian on bounded domains, establishing conditions for existence, non-existence, a priori estimates, and symmetry properties.

Contribution

It provides new existence and non-existence results, along with a priori estimates and symmetry analysis for fractional Laplacian systems, advancing understanding in this area.

Findings

Existence and non-existence conditions established

A priori estimates of Gidas-Spruck type derived

Symmetry properties proved for solutions

Abstract

In this paper we study strongly indefinite systems involving the fractional Laplacian on bounded domains. We obtain existence and non-existence results, $a priori$ estimates of Gidas-Spruck type, and the symmetric property.