Symmetry breaking solutions of nonlinear elliptic systems

Javier Bracho, Mónica Clapp, Wacław Marzantowicz

DOI: http://dx.doi.org/10.12775/TMNA.2005.030

Abstract


We consider nonlinear elliptic systems with Dirichlet boundary condition on
a bounded domain in $\mathbb R^{N}$ which is invariant with respect to the
action of some group $G$ of orthogonal transformations. For every subgroup
$K$ of $G$ we give a simple criterion for the existence of infinitely many
solutions which are $K$-invariant but not $G$-invariant. We include
a detailed discussion of the case $N=3$.

Keywords


Variational elliptic systems; symmetry breaking

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