Connected sets of solutions of symmetric elliptic systems

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.