Existence of least-energy sign-changing solutions for Schrödinger-Poisson system with critical growth

Abstract

In this paper, we study the following Schrödinger-Poisson system{−Δu+V(x)u+λϕu=|u|4u+μf(u),x∈R3,−Δϕ=u2,x∈R3, where V(x) is a smooth function and μ,λ>0. Under suitable conditions on f, by using constraint variational method and the quantitative deformation lemma, if μ is large enough, we obtain a least-energy sign-changing (or nodal) solution uλ to this problem for each λ>0, and its energy is strictly larger than twice that of the ground state solutions. Moreover, we study the asymptotic behavior of uλ as the parameter λ↘0.