Multiple solutions for Schrödinger-Poisson systems with indefinite potential and combined nonlinearity

In this paper, we study the existence of infinitely many solutions for the following nonlinear Schrödinger-Poisson system{−△u+V(x)u+ϕu=f(x,u)+g(x,u),x∈R3,−△ϕ=u2,lim|x|→∞⁡ϕ(x)=0, where the potential V may be unbounded from below. Under some mild conditions on the nonlinear terms f and g, we obtain infinitely many solutions of this system. Recent results from the literature are generalized and significantly improved.