Structure of sets of solutions of parametrised semi-linear elliptic systems on spheres

TL;DR

This paper investigates the structure and bifurcation of solutions in parametrized symmetric semi-linear elliptic systems on spheres, utilizing equivariant Rabinowitz Alternative to identify conditions for unbounded solution sets.

Contribution

It introduces a framework for analyzing solution sets of symmetric elliptic systems on spheres and establishes bifurcation conditions using equivariant Rabinowitz Alternative.

Findings

Identification of conditions for bifurcation of unbounded solutions

Application of equivariant Rabinowitz Alternative to elliptic systems

Analysis of solution structure based on potential critical orbits

Abstract

In this paper we study a parametrised non-cooperative symmetric semi-linear elliptic system on a sphere. Assuming that there exist critical orbits of the potential, we study the structure of the sets of solutions of the system. In particular, using the equivariant Rabinowitz Alternative we formulate sufficient conditions for a bifurcation of unbounded sets of solutions.