Semiclassical ground states for nonlinear Schrödinger-Poisson systems
Texas State University, Department of Mathematics
In this article, we study the Schrödinger-Poisson system -ε2∆u + V(x)u + φ(x)u = Q(x)u3, x ∈ ℝ3, -ε2∆φ = u2, x ∈ ℝ3, where ε > 0 is a parameter, V and Q are positive bounded functions. We establish the existence of ground states for ε small, and describe the concentration phenomena of ground states as ε → 0.
Schrödinger-Poisson system, Variational method, Concentration, Nehari manifold
Zhang, H., & Zhang, F. (2018). Semiclassical ground states for nonlinear Schrödinger-Poisson systems. <i>Electronic Journal of Differential Equations, 2018</i>(61), pp. 1-15.