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Unbounded sets of solutions of non-cooperative elliptic systems on spheres

2015; Elsevier BV; Volume: 259; Issue: 7 Linguagem: Inglês

10.1016/j.jde.2015.04.012

ISSN

1090-2732

Autores

Sławomir Rybicki, Piotr Stefaniak,

Tópico(s)

Stability and Controllability of Differential Equations

Resumo

The aim of this paper is to show that any continuum of nontrivial solutions of a non-cooperative system of elliptic equations on the sphere S n − 1 , bifurcating from the set of trivial solutions, is unbounded. Moreover, we characterize bifurcation points of this system at which the global symmetry-breaking phenomenon occurs. As the main tool we use the degree for SO ( 2 ) -invariant strongly indefinite functionals defined in [13] .

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