A computer assisted proof of the symmetries of least energy nodal solutions on squares

Abstract

Using a Lyapunov-Schmidt reduction on an asymptotic Nehari manifold and verified computations, we prove that the least energy nodal solutions to LaneEmden equation −∆u = |u| p−2u with zero Dirichlet boundary conditions on a square are odd with respect to one diagonal and even with respect to the other one when p is close to 2.