Positive solutions of asymptotically linear Schrödinger-Poisson systems with a radial potential vanishing at infinity

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

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