Global bifurcation index of critical orbit of strongly indefinite functional

2018/09/26 by Anna Gołȩbiewska, Gołębiewska, Anna, Piotr Stefaniak +1
Mathematics · #35J50 (Secondary) #58E09 (Primary) #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1809.09950

openalex publication_date 2018/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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