Positive solution for a nonlinear stationary Schrödinger-Poisson system in R³

In this paper, we are concerned with the following problem(P) -Δ u + V(x)u+λ φ (x) u =f(x,u), x∈ R³ -Δφ = u², lim|x|→ +∞φ(x)=0,where λ >0 is a parameter, the potential $V(x)$ may not beradially symmetric, and $f(x,s)$ is asymptotically linear withrespect to s at infinity. Under some simple assumptions on V andf, we prove that the problem (P) has a positive solution forλ small and has no any nontrivial solution for λlarge.