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 study orbits of nonconstant solutions of a nonlinear Neumann problem.

中文翻译：

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对称椭圆系统的连通解集

本文的目的是双重的。首先，我们研究给定的关键轨道族中某些不变函数的关键轨道的连通集的分支。我们使用等变分叉理论的技术来获得对称梯度算子的Rabinowitz类型替代。第二个目的是将抽象结果应用于研究非线性Neumann问题的非恒定解的轨道。