The concentration behavior of ground states solution for a Schrödinger system of Hamiltonian type - Qiu, Ruowen; Yu, Yangyang; Zhao, Fukun (Topological Methods in Nonlinear Analysis, 2025)
In this paper, we consider the following nonlinear Schrödinger system of Hamiltonian type equation* cases -ε^2 Δ u+u+V(x)v=H_v(u,v), & xR^N, -ε^2 Δ v+v+V(x) u= H_u(u, v),& xR^N, u(x)→0 and v(x)→0 & as |x|→∞, cases equation* where ε> 0 is a small parameter, VC^1(R^N, R), HC^1(R×R,R) and (u,v)R^2. Under only a local condition that V has a local trapping potential well, a ground state z_ε=(u_ε,v_ε) of the above Schrödinger system is obtained via a combination of linking-type arguments with the generalized Nehari manifold. Moreover, we also show that ground state solution z_ε concentrating around the local minimum points of the potential V as ε→ 0^+.