(untitled) (Journal of Partial Differential Equations, 2023)
In this paper, we consider the following Schrödinger-Poisson system equation*cases -Δ u + ηφ u = f(x,u) + u^5,& xΩ, -Δφ=u^2,& xΩ, u = φ =0,& xΩ, casesequation* where Ω is a smooth bounded domain in R^3, η=±1 and the continuous function f satisfies some suitable conditions. Based on the Mountain pass theorem, we prove the existence of positive ground state solutions.