Abstract In this paper we study the global bifurcation from a critical orbit of a strongly indefinite functional. This problem arises in considering the bifurcations of solutions to non-cooperative semi-linear elliptic systems with Neumann boundary conditions. We define an index of an orbit in terms of an equvariant degree and establish its relationship with the index of a critical point of the mapping restricted to the space normal to the orbit. We use the obtained results to prove the bifurcation of nontrivial solutions to the Neumann problem. We consider also the existence of unbounded sets of solutions of such systems.

中文翻译：

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非合作半线性诺依曼问题解的轨道的全局分岔

摘要 在本文中，我们研究了从一个强不定泛函的临界轨道的全局分岔。这个问题是在考虑具有 Neumann 边界条件的非合作半线性椭圆系统的解的分岔时出现的。我们根据等变度来定义轨道的索引，并建立其与映射的临界点索引的关系，该索引限于轨道法线空间。我们使用获得的结果来证明 Neumann 问题的非平凡解的分岔。我们还考虑了此类系统的无界解集的存在。