Multiplicity of small negative-energy solutions for a class of nonlinear Schrödinger–Poisson systems

摘要

This paper deals with the following nonlinear Schrödinger–Poisson systems-Δu+V(x)u+K(x)ϕ(x)u=H(x)f(x,u),inR3,-Δϕ=K(x)u2,inR3,where V(x), K(x) and H(x) are nonnegative continuous functions. Under appropriate assumptions on V(x), K(x),H(x) and f(x,u), we prove the existence of infinitely many small negative-energy solutions by using the variant fountain theorem established by Zou. Recent results from the literature are extended.