Non-radial sign-changing solutions for the Schroedinger-Poisson problem in the semiclassical limit

TL;DR

This paper proves the existence of complex nonradial, sign-changing solutions with multiple peaks for the Schroedinger-Poisson system in higher dimensions, using Lyapunov-Schmidt reduction.

Contribution

It introduces a novel construction of multi-peak, sign-changing solutions with symmetric configurations collapsing to a single point.

Findings

Existence of nonradial sign-changing solutions in N>=3

Construction of multi-peak solutions with symmetric arrangements

Solutions collapse to the same point in the limit

Abstract

We study the existence of nonradial sign-changing solutions to the Schroedinger-Poisson system in dimension N>=3. We construct nonradial sign-changing multi-peak solutions whose peaks are displaced in suitable symmetric configurations and collapse to the same point. The proof is based on the Lyapunov-Schmidt reduction.