Title: | Non-symmetric low-index solutions
for a symmetric boundary value problem |

Authors: | G. Arioli, H. Koch |

Abstract: |
We consider the equation Δu=wu^{3} on a square domain
in R^{2}, with Dirichlet boundary conditions,
where w is a given positive function
that is invariant under all (Euclidean) symmetries of the square.
This equation is shown to have a solution u,
with Morse index 2, that is neither symmetric
nor antisymmetric with respect to any nontrivial symmetry of the square.
Part of our proof is computer-assisted.
An analogous result is proved for index 1. |

Paper: | Preprint, programs and data files |