Schrödinger–Poisson system with zero mass and convolution nonlinearity in R2

Article type: Research Article

Authors: Yang, Heng^{; *}

Affiliations: Public Basic Course Department, Hunan Polytechnic of Environment and Biology, Hengyang, Hunan 421005, P.R. China

Correspondence: [*] Corresponding author. E-mail: yangheng_2021@yeah.net.

Abstract: In this paper, we prove the existence of nontrivial solutions and ground state solutions for the following planar Schrödinger–Poisson system with zero mass −Δu+ϕu=(Iα∗F(u))f(u),x∈R2,Δϕ=u2,x∈R2, where α∈(0,2), Iα:R2→R is the Riesz potential, f∈C(R,R) is of subcritical exponential growth in the sense of Trudinger–Moser. In particular, some new ideas and analytic technique are used to overcome the double difficulties caused by the zero mass case and logarithmic convolution potential.

Keywords: Planar Schrödinger–Poisson system, Logarithmic convolution potential, zero mass

DOI: 10.3233/ASY-211741

Journal: Asymptotic Analysis, vol. 130, no. 1-2, pp. 1-21, 2022