Positive solutions of asymptotically linear Schrödinger–Poisson systems with a radial potential vanishing at infinity Original Research Article

In this paper, we study the Schrödinger–Poisson system equation(SP) View the MathML source{−Δu+V(x)u+λϕ(x)u=K(x)f(u),inR3,−Δϕ=u2,u>0,inR3, Turn MathJax on and prove the existence of positive solutions for system (SP) when the nonlinearity ff has growth at most linear for λλ small, allowing the potential V(x)V(x) to vanish at infinity. In addition, also we obtain the nonexistence of a nontrivial positive solution for View the MathML sourceλ≥14.