Sign-changing solutions for nonlinear Schrödinger–Poisson systems with subquadratic or quadratic growth at infinity. (September 2020) - Gu, Lihua; Jin, Hua; Zhang, Jianjun
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.