Small solutions of nonlinear Schrodinger equations near first excited states

PDE Seminar
Tuesday, August 31, 2010 - 15:00
1 hour (actually 50 minutes)
Skiles 114
Department of Mathematics, University of British Columbia
 Consider a nonlinear Schrodinger equation in $R^3$  whose linear part has three or more eigenvalues satisfying some resonance conditions. Solutions which are initially small  in $H^1 \cap L^1(R^3)$ and inside a neighborhood of the first excited state family are shown to converge to either a first excited state or a ground state at time infinity. An essential part of our analysis is on the linear and nonlinear estimates near nonlinear excited states, around which the linearized operators have eigenvalues with nonzero real parts and their corresponding eigenfunctions are not uniformly localized in space. This is a joint work with Kenji Nakanishi and  Tuoc Van Phan.The preprint of the talk is available at