Positive and sign-changing clusters around saddle points of the potential for nonlinear elliptic problems

Details Positive and sign-changing clusters around saddle points of the potential for nonlinear elliptic problems Positive and sign-changing clusters around saddle points of the potential for nonlinear elliptic problems

2009-07-03

arxiv.org/abs/0907.0558v1

Mathematics

Analysis of PDEs

Scientific paper

We study the existence of positive and sign-changing multipeak solutions for the stationary Nonlinear Schroedinger Equation. Here no symmetry on $V$ 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.

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