%0 Journal Article
%T A nodal solution of the scalar field equation at the second minimax level
%A Kanishka Perera
%A Cyril Tintarev
%J Mathematics
%D 2014
%I arXiv
%X We prove the existence of a sign-changing eigenfunction at the second minimax level of the eigenvalue problem for the scalar field equation under a slow decay condition on the potential near infinity. The proof involves constructing a set consisting of sign-changing functions that is dual to the second minimax class. We also obtain a nonradial sign-changing eigenfunction at this level when the potential is radial.
%U http://arxiv.org/abs/1402.2356v1