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

This paper is concerned with the Schrödinger–Poisson system −Δu + ϕu = λu + μ|u|2u and −Δϕ = u2 setting on a bounded domain Ω ⊂ R 3 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 μ ̄ > 0 such that for all (λ , μ) ∈ (− ∞ , λ 1 ) × ( μ ̄ , + ∞) , the above system has one least energy sign-changing solution, where λ1 > 0 is the first eigenvalue of − Δ , H 0 1 (Ω) . The results of this paper are complementary to those in Alves and Souto [Z. Angew. Math. Phys. 65, 1153–1166 (2014)]. [ABSTRACT FROM AUTHOR]