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Global Bifurcations of Solutions of Elliptic Differential Equations

1998; Elsevier BV; Volume: 217; Issue: 1 Linguagem: Inglês

10.1006/jmaa.1997.5704

1096-0813

Sławomir Rybicki,

Nonlinear Differential Equations Analysis

The aim of this article is to prove global bifurcation theorems forS1-equivariant potential operators of the form “compact perturbation of identity.” As an application we prove that components of the set of nontrivial solutions of system[formula]which bifurcate from the set of trivial solutions are unbounded in suitably chosen space. The important point to note here is that our results apply only to systems with an even number of equations. As the main tool we use degree theory forS1-equivariant potential operators constructed by the author in [16] and developed in [17].