Semi-classical states for Schrödinger-Poisson systems on R^3
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Date
2016-03-17
Authors
Zhu, Hongbo
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In 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.
Description
Keywords
Schrödinger-Poisson system, Semi-classical states, Variational method
Citation
Zhu, H. (2016). Semi-classical states for Schrödinger-Poisson systems on R^3. <i>Electronic Journal of Differential Equations, 2016</i>(75), pp. 1-15.
Rights
Attribution 4.0 International