Global bifurcation from an orbit of solutions to non-cooperative semi-linear Neumann problem

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 eq...

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Bibliographic Details
Published in:Journal of Differential Equations 2020-05, Vol.268 (11), p.6702-6728
Main Authors: Gołȩbiewska, Anna, Stefaniak, Piotr
Format: Article
Language:English
Subjects:
Bifurcation theory
Equivariant degree
Systems of elliptic equations
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Summary: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.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2019.11.053