Existence of multiple positive solutions to nonhomogeneous Schrödinger–Poisson system

In this paper, we consider the existence of multiple solutions to the following nonhomogeneous generalized Schrödinger–Poisson system-Δu+Ku+qϕf(u)=g(u)+h(x),inR3,-Δϕ=2qF(u),inR3,where q⩾0q⩾0is a parameter, 0≠h(x)=h(|x|)∈L2(R3), and g   is asymptotically linear or superliner at infinity. We show that there exists q0>0q0>0 such that the system has at least two positive radial solutions for q∈[0,q0)q∈[0,q0).