Gianni Arioli, Hans Koch Non-symmetric low-index solutions for a symmetric boundary value problem (1899K, plain TeX, with eps figures) ABSTRACT. We consider the equation Δu=wu3 on a square domain in R2, 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.