Sufficient and necessary conditions for ground state sign-changing solutions to the Schrödinger–Poisson system with cubic nonlinearity on bounded domains. (January 2022)

• Record Type: Journal Article
• Authors: Yu, Shubin; Zhang, Ziheng
• Is Part Of: Applied mathematics letters. Volume 123(2022)
• Publication Date: 2022-01
• Subjects: Schrödinger–Poisson system -- Cubic nonlinearity -- Sign-changing solution; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107570
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper we are interested in the existence of ground state sign-changing solutions to the following Schrödinger–Poisson system − Δ u + ϕ u = λ u + μ | u | 2 u in Ω − Δ ϕ = u 2 in Ω u = ϕ = 0 on ∂ Ω, where Ω is a bounded smooth domain of R 3, μ > 0, λ < λ 1 and λ 1 is the first eigenvalue of − Δ, H 0 1 ( Ω ) . Using construction technique, we show that the above system possesses one ground state sign-changing solution if and only if μ > 0, which improves the recent results by Khoutir (2021).