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In this paper we consider a resonance problem, in a generic regime, in theconsideration of relaxation of ground states of semilinear Schrodingerequations. Different from previous results, our consideration includes thepresence of resonance, resulted by overlaps of frequencies of different states.All the known key results, proved under non-resonance conditions, have beenrecovered uniformly. These are achieved by better understandings of normal formtransformation and Fermi Golden rule. Especially, we find that if certaindenominators are zeros (or small), resulted by the presence of resonances (orclose to it), then cancellations between terms make the correspondingnumerators proportionally small.

A Resonance Problem in Relaxation of Ground States of Nonlinear Schrodinger Equations