Symmetry breaking solutions of nonlinear elliptic systems (Q812902)

The semi-linear elliptic systems with Dirichlet boundary condition on a bounded smooth domain is considered. For every subgroup \(K\) of some group \(G\) of orthogonal transformations a criterion for the existence of infinitely many solutions which are \(K\)-invariant but not \(G\)-invariant is obtained by application of methods of the group theory. The conditions of existence of infinitely many intertwining solutions is founded too.