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Multiple solutions for a critical quasilinear equation with Hardy potential
November 2019, 12(7): 2005-2017. doi: 10.3934/dcdss.2019129
Global symmetry-breaking bifurcations of critical orbits of invariant functionals
Anna Goƚȩbiewska 1,, , Norimichi Hirano 2, and Sƚawomir Rybicki 1,
Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, PL-87-100 Toruń, ul. Chopina 12/18, Poland
Department of Mathematics, Graduate School of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogayaku, Yokohama, Japan
Received October 2017 Revised April 2018 Published December 2018
Fund Project: Partially supported by the National Science Center, Poland, under grant DEC-2012/05/B/ST1/02165.
In this article we present a method of study of a global symmetry-breaking bifurcation of critical orbits of invariant functionals. As a topological tool we use the degree for equivariant gradient maps. We underline that many known results on bifurcations of non-radial solutions of elliptic PDE's from the families of radial ones are consequences of our theory.
Keywords: Equivariant bifurcation theory, global bifurcation, symmetry-breaking bifurcation, degree for equivariant gradient maps, non-radial bifurcations.
Mathematics Subject Classification: Primary: 58E09; Secondary: 35J50.
Citation: Anna Goƚȩbiewska, Norimichi Hirano, Sƚawomir Rybicki. Global symmetry-breaking bifurcations of critical orbits of invariant functionals. Discrete & Continuous Dynamical Systems - S, 2019, 12 (7) : 2005-2017. doi: 10.3934/dcdss.2019129
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Anna Goƚȩbiewska Norimichi Hirano Sƚawomir Rybicki