Ground state solutions for Schrödinger–Poisson system with critical exponential growth in [formula omitted

Abstract

This paper gives weak sufficient conditions to get the existence of ground state solutions for the following planar Schrödinger–Poisson system −Δu+V(x)u+ϕu=f(x,u),x∈R2,Δϕ=u2,x∈R2,where V∈C(R2,[0,∞)) is axially symmetric and f∈C(R2×R,R) is of critical exponential growth in the sense of Trudinger–Moser inequality. Especially, some new estimates involving the Moser’s sequence of functions are given to get some suitable upper bound for the mountain pass level. Our theorem extends and improves the results of de Figueiredo et al. (1995) and of Chen and Tang (2020).