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 - Δ u + Ku + q ϕ f ( u ) = g ( u ) + h ( x ) , in R 3 , - Δ ϕ = 2 qF ( u ) , in R 3 , where q ⩾ 0 is a parameter, 0 ≠ h ( x ) = h ( | x | ) ∈ L 2 ( R 3 ) , and g is asymptotically linear or superliner at infinity. We show that there exists q 0 > 0 such that the system has at least two positive radial solutions for q ∈ [ 0 , q 0 ) . [ABSTRACT FROM AUTHOR]