On the Schrödinger-Poisson system with indefinite potential and 3-sublinear nonlinearity

Abstract

We consider a class of stationary Schrödinger-Poisson systems with a general nonlinearity f (u) and coercive sign-changing potential V so that the Schrödinger operator −∆ +V is indefinite. Previous results in this framework required f to be strictly 3-superlinear, thus missing the paramount case of the Gross-Pitaevskii-Poisson system, where f (t) = |t| 2 t; in this paper we fill this gap, obtaining non-trivial solutions when f is not necessarily 3-superlinear.

Existence Solutions for a Class of Schrödinger-Maxwell Systems with Steep Well Potential

“…Very recently, Liu and Mosconi [18] considered the following system with a coercive sign-changing potential and a 3sublinear nonlinearity:…”

Existence and concentration of solution for Schrödinger-Poisson system with local potential

“…If the potential is radial symmetry and has asymptotical behavior at infinity, Li et al [23] studied the existence of infinitely many sign-changing solutions. For other related nonlocal variational problems, we refer the interested readers to see [3,10,20,24,28,29,33,41,42] and the references therein.…”

Existence and concentration of solution for Schrödinger-Poisson system with local potential

“…If the potential is radial symmetry and has asymptotical behavior at infinity, Li et al [23] studied the existence of infinitely many sign-changing solutions. For other related nonlocal variational problems, We refer the interested readers to see [3,10,16,24,28,29,33] and the references therein.…”