arXiv subjects
Publications and source records attributed to M. Ghimenti.
We show that the number of low energy solutions of a double singularly perturbed Schroedinger Maxwell system type on a smooth 3 dimensional manifold (M,g) depends on the topological properties of the manifold. The result is obtained via Lusternik Schnirelmann category theory.
In this paper we investigate the dynamics of solitons occurring in the nonlinear Schroedinger equation when a parameter h->0. We prove that under suitable assumptions, the the soliton approximately follows the dynamics of a point particle, namely, the motion of its barycenter $q_h(t)$ satisfies the equation $ddot{q}_h(t)+\nabla V(q_h(t))=H_h(t)$ where $\sup_{t\in R} |H_h(t)| -> 0$ as h->0.