Existence and Concentration of Solutions For Sublinear Schrödinger-Poisson Equations

We concern the sublinear Schrödinger-Poisson equations {−Δu+λV(x)u+ϕu=f(x,u)inℝ3−Δϕ=u 2inℝ3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\{ \begin{gathered} - \Delta u + \lambda V\left( x \right)u + \phi u = f\left( {x,u} \right)in{\mathbb{R}^3} \hfill \\ - \Delta \phi = {u^2}in{\mathbb{R}^3} \hfill \\ \end{gathered} \right.$$\end{document} where λ > 0 is a parameter, V ∈ C(R3,[0,+∞)), f ∈ C(R3×R,R) and V-1(0) has nonempty interior. We establish the existence of solution and explore the concentration of solutions on the set V-1(0) as λ → ∞ as well. Our results improve and extend some related works.