English

A nodal solution of the scalar field equation at the second minimax level

Analysis of PDEs 2017-05-04 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1402.2356,
  title  = {A nodal solution of the scalar field equation at the second minimax level},
  author = {Kanishka Perera and Cyril Tintarev},
  journal= {arXiv preprint arXiv:1402.2356},
  year   = {2017}
}