### Symmetry breaking solutions of nonlinear elliptic systems

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 $N=3$.

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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