Article ID Journal Published Year Pages File Type
841046 Nonlinear Analysis: Theory, Methods & Applications 2011 11 Pages PDF
Abstract

In this paper, we study the Schrödinger–Poisson system equation(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 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 λ≥14.

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