Global bifurcation index of critical orbit of strongly indefinite functional

In this paper we study an index of a critical orbit, defined in terms of the degree for invariant strongly indefinite functionals. We establish a relationship of this index with the index of a critical point of the mapping restricted to the space normal to the orbit. The second aim of the article is...

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Bibliographic Details
Published in:arXiv.org 2018-09
Main Authors: Gołębiewska, Anna, Stefaniak, Piotr
Format: Article
Language:English
Subjects:
Bifurcations
Boundary conditions
Critical point
Mapping
Nonlinear systems
Online Access:Get full text
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Summary:In this paper we study an index of a critical orbit, defined in terms of the degree for invariant strongly indefinite functionals. We establish a relationship of this index with the index of a critical point of the mapping restricted to the space normal to the orbit. The second aim of the article is to use the index of a critical orbit to prove the bifurcation of nontrivial solutions of nonlinear elliptic systems with Neumann boundary conditions. We consider also the existence of unbounded sets of solutions of such systems.
ISSN:2331-8422