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Symmetry-breaking at positive solutions

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Abstract

We consider symmetry-breaking bifurcations at positive solutions of semilinear elliptic boundary value problems in a ball, with Dirichlet boundary conditions. We prove that symmetry-breaking can only occur by bifurcation of axisymmetric solutions. We also obtain sufficient conditions for such symmetry-breaking.

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Authors and Affiliations

  1. Instituut voor Theoretische Mechanica, Rijksuniversiteit Gent, Krijgslaan 281, B-9000, Gent, Belgium

    A. Vanderbauwhede

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  1. A. Vanderbauwhede
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Dedicated to Professor H. Knobloch at the occasion of his 60th birthday

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Vanderbauwhede, A. Symmetry-breaking at positive solutions. Z. angew. Math. Phys. 38, 315–326 (1987). https://doi.org/10.1007/BF00945416

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  • DOI: https://doi.org/10.1007/BF00945416

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