Structure of sets of solutions of parametrised semi-linear elliptic systems on spheres. (November 2021)

• Record Type: Journal Article
• Authors: Gołȩbiewska, Anna; Stefaniak, Piotr
• Is Part Of: Nonlinear analysis. Volume 212(2021)
• Publication Date: 2021-11
• Subjects: primary 35J50 -- secondary 35B32; Non-cooperative elliptic systems -- Global bifurcations -- Equivariant degree; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112451
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we study a parametrised non-cooperative symmetric semi-linear elliptic system on a sphere. Assuming that there exist critical orbits of the potential, we study the structure of the sets of solutions of the system. In particular, using the equivariant Rabinowitz alternative we formulate sufficient conditions for a bifurcation of unbounded sets of solutions.