(untitled) (Journal of Partial Differential Equations, 2025)
In this paper, we consider the following nonhomogeneous Schrödinger-Poisson system cases-∆u+u+η φ u=u^5+λ f(x), & xR^3, -∆φ=u^2, & xR^3, caseswhere η e 0, λ>0 is a real parameter and f∈L^65 (R^3) is a nonzero nonnegative function. By using the Mountain Pass theorem and variational method, for λ small, we show that the system with η >0 has at least two positive solutions, the system with η