Zhu, Hongbo2023-06-162023-06-162016-03-17Zhu, H. (2016). Semi-classical states for Schrödinger-Poisson systems on R^3. <i>Electronic Journal of Differential Equations, 2016</i>(75), pp. 1-15.1072-6691https://hdl.handle.net/10877/16947In this article, we study the nonlinear Schrödinger-Poisson equation -ε2∆u + V(x)u + φ(x)u = ƒ(u), x ∈ ℝ3, -ε2∆φ = u2, lim |x|→∞ φ(x) = 0. Under suitable assumptions on V(x) and ƒ(x), we prove the existence of ground state solution around local minima of the potential V(x) as ε → 0. Also, we show the exponential decay of ground state solution.Text15 pages1 file (.pdf)enAttribution 4.0 InternationalSchrödinger-Poisson systemSemi-classical statesVariational methodArticle