Constraint Minimizers Of Perturbed Gross-Pitaevskii Energy Functionals In R~N

This thesis is concerned with constraint minimizers of an L2-critical minimization problem under an L2-suberitical perturbation,for which we study the existence of minimizers and analyze the concentration behavior of minimizers.Roughly speaking,we consider constraint minimizers of the following L2-critical minimization problem Here the Gross-Pitaevskii(GP)energy functional E(u)contains an L2-suberitical perturbation and satisfiesNext,we analyze rigorously the concentration behavior of minimizers as ???*for the case where b>0,which shows that the concentration rates are determined mainly by the suberitical perturbation,instead of the local profiles of the potential V(x).Our results indicate that the sub-critical perturbation influences mainly the blow up rates of minimizers,and however the potential V(x)influences mainly the location where the minimizers blow up.This is one of the main con-tributions in this thesis.