Codice 36/2010 Titolo Non-Symmetric low-index solutions for a symmetric boundary value problem Data 2010-11-11 Autore/i Arioli, G.; Koch, H. Link Download full text Abstract We consider the equation -Laplacian(u)=w*u^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.