Non-radial multipeak positive solutions for the Schrödinger–Poisson problem

Abstract

In this paper, we consider the following Schrödinger–Poisson problem{−ε2Δu+V(x)u+Φu=up,x∈RN,−ΔΦ=u2,x∈RN, where ε>0 is a small parameter, N≥3, and V(x) is a potential function. This system describes some physical phenomena such as quantum mechanics models. We construct non-radial positive solutions, whose components may have spikes clustering at the same point as ε→0+, but the distance between them divided by ε will go to infinity.