Least energy sign-changing solutions for a class of Schrödinger–Poisson system on bounded domains

Abstract

This paper is concerned with the Schrödinger–Poisson system −Δu + ϕu = λu + μ|u|2u and −Δϕ = u2 setting on a bounded domain Ω⊂R3 with smooth boundary and λ,μ∈R being parameters. By using variational techniques in combination with the nodal Nehari manifold method, we show the existence of μ̄>0 such that for all (λ,μ)∈(−∞,λ1)×(μ̄,+∞), the above system has one least energy sign-changing solution, where λ1 > 0 is the first eigenvalue of −Δ,H01(Ω). The results of this paper are complementary to those in Alves and Souto [Z. Angew. Math. Phys. 65, 1153–1166 (2014)].