Positive and sign-changing clusters around saddle points of the potential for nonlinear elliptic problems
Analysis of PDEs
2009-07-06 v1
Abstract
We study the existence of positive and sign-changing multipeak solutions for the stationary Nonlinear Schroedinger Equation. Here no symmetry on is assumed. It is known that this equation has positive multipeak solutions with all peaks approaching a local maximum of the potential. It is also proved that solutions alternating positive and negative spikes exist in the case of a minima. The aim of this paper is to show the existence of both positive and sign-changing multipeak solutions around a nondegenerate saddle point of the external potential.
Keywords
Cite
@article{arxiv.0907.0558,
title = {Positive and sign-changing clusters around saddle points of the potential for nonlinear elliptic problems},
author = {Teresa D'Aprile and David Ruiz},
journal= {arXiv preprint arXiv:0907.0558},
year = {2009}
}