Sign-changing solutions for nonlinear Schrödinger–Poisson systems with subquadratic or quadratic growth at infinity. (September 2020)

• Record Type: Journal Article
• Authors: Gu, Lihua; Jin, Hua; Zhang, Jianjun
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: 35J60 -- 35J20; Schrödinger–Poisson system -- Invariant sets of descending flow -- Sign-changing solutions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111897
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper is dedicated to investigating the existence of sign-changing solutions to the following Schrödinger–Poisson system − Δ u + V ( x ) u + λ ϕ u = f ( u ) in R 3, − Δ ϕ = u 2 in R 3, where λ > 0 and f is subquadratic or quadratic at infinity. By using the method of invariant sets of descending flow, we prove that the problem above admits multiple radial sign-changing solutions in the subquadratic case as λ small. As for the quadratic case, by virtue of a perturbation argument, we show that this problem admits at least one sign-changing solution as λ small.