Small solutions of nonlinear Schrodinger equations near first excited states

Thursday, June 30, 2011 - 2:00pm - 2:30pm
Lind 305
Tuoc Phan (University of Tennessee)
Consider a nonlinear Schrodinger equation in R3 whose linear part has three or more eigenvalues satisfying some resonance conditions. Solutions which are initially small in H1 \ L1(R3) 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.
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