Ground state sign-changing solutions for asymptotically cubic or super-cubic Schrödinger-Poisson systems without compact condition

This paper is dedicated to studying the following Schrödinger-Poisson system {−△u+V(x)u+ϕu=K(x)f(u),x∈R3,−△ϕ=u2,x∈R3, where V,K∈C(R3,R) and f∈C(R,R). Under mild assumptions on the decay rate of V(x), we establish the existence of one ground state sign-changing solution with precisely two nodal domains, by using a weaker growth condition lim∣t∣→∞∫0tf(s)ds∣t∣3=∞, instead of the usual super-cubic condition lim∣t∣→∞∫0tf(s)ds∣t∣4=∞. Our result unifies both asymptotically cubic and super-cubic cases, which generalizes and improves the corresponding ones in the literatures.