Symmetry of n-mode positive solutions for two-dimensional H\'enon type systems

TL;DR

This paper establishes symmetry properties for positive solutions of certain elliptic systems and demonstrates the existence of multiple solutions in Hénon-type systems, advancing understanding of solution structures in nonlinear PDEs.

Contribution

It proves symmetry results for n-mode positive solutions and shows the existence of multiple solutions in Hénon systems under cooperative nonlinearities.

Findings

Symmetry of solutions is established for a broad class of elliptic systems.

Multiple n-mode positive solutions are proven to exist in Hénon systems.

The results extend previous symmetry and existence theories in nonlinear elliptic PDEs.

Abstract

We provide a symmetry result for n-mode positive solutions of a general class of semi-linear elliptic systems under cooperative conditions on the nonlinearities. Moreover, we apply the result to a class of H\'enon systems and provide the existence of multiple n-mode positive solutions.