2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57057We consider a nonlinear Schrödinger equation with a bounded local potential in $R^3$. The linear Hamiltonian is assumed to have three or more bound states with the eigenvalues satisfying some resonance conditions. Suppose that the initial data is localized and small of order $n$ in $H^1$, and that its ground state component is larger than $n^{3-ε}$ with $ε>0$ small. We prove that the solution will converge locally to a nonlinear ground state as the time tends to infinity.Mathematical PhysicsAnalysis of PDEs35Q40; 35Q55text