  In this paper we consider a resonance problem, in a generic regime, in the
consideration of relaxation of ground states of semilinear Schrodinger
equations. Different from previous results, our consideration includes the
presence of resonance, resulted by overlaps of frequencies of different states.
All the known key results, proved under non-resonance conditions, have been
recovered uniformly. These are achieved by better understandings of normal form
transformation and Fermi Golden rule. Especially, we find that if certain
denominators are zeros (or small), resulted by the presence of resonances (or
close to it), then cancellations between terms make the corresponding
numerators proportionally small.
