Infinitely Many Solutions of Schrödinger-Poisson Equations with Critical and Sublinear Terms

Abstract EN

In this paper, we study the following Schrödinger-Poisson equations −Δu+u+ϕu=u5+λaxup−1u,x∈ℝ3,−Δϕ=u2,x∈ℝ3, where the parameter λ>0 and p∈0,1.

When the parameter λ is small and the weight function ax fulfills some appropriate conditions, we admit the Schrödinger-Poisson equations possess infinitely many negative energy solutions by using a truncation technology and applying the usual Krasnoselskii genus theory.

In addition, a byproduct is that the set of solutions is compact.