Ground state solutions of Schrödinger–Poisson systems with asymptotically constant potential

Article type: Research Article

Authors: Lin, Xiaoyan^a | He, Yubo^{a; *} | Tang, Xianhua^b

Affiliations: [a] Department of Mathematics, Huaihua College, Huaihua, Hunan 418008, China. E-mails: xiaoyanlin98@hotmail.com, heyinprc80@hotmail.com | [b] School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, P.R. China. E-mail: tangxh@mail.csu.edu.cn

Correspondence: [*] Corresponding author. E-mail: heyinprc80@hotmail.com.

Abstract: This paper is focused on the following Schrödinger–Poisson system −Δu+V(x)u+ϕu=f(u),x∈R3,−Δϕ=u2,x∈R3, where V(x) is weakly differentiable and tends asymptotically to a constant and f∈C(R,R). By introducing some new tricks, we prove that the above system admits a ground state solution under some mild assumptions on V and f. Our results generalize and improve the existing ones in the literature.

Keywords: Schrödinger–Poisson system, ground state solution, Pohozaev type identity

DOI: 10.3233/ASY-201639

Journal: Asymptotic Analysis, vol. 124, no. 1-2, pp. 29-49, 2021