Connected sets of solutions of symmetric elliptic systems

2019/11/28 by Gołębiewska, Anna, Rybicki, Sławomir, Stefaniak, Piotr
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.12632

Abstract

The purpose of this paper is twofold. First we study bifurcations of connected sets of critical orbits of some invariant functional from a given family of critical orbits. We use techniques of equivariant bifurcation theory to obtain a Rabinowitz type alternative for symmetric gradient operators. The second aim is to apply the abstract results to studying orbits of nonconstant solutions of a nonlinear Neumann problem.

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• Unbounded sets of solutions of non-cooperative elliptic systems on symmetric spaces
• Bifurcations from degenerate orbits of solutions of nonlinear elliptic systems
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• Bifurcations from the orbit of solutions of the Neumann problem