%0 Journal Article
%T Constraint Minimizers of the Gross-Pitaevskii Functional with Logarithmic Convolution and Ringed Shape Potential
%A Xuanxuan Li
%J Open Access Library Journal
%V 13
%N 2
%P 1-13
%@ 2333-9721
%D 2026
%I Open Access Library
%R 10.4236/oalib.1114915
%X We consider a constrained variational problem where the energy functional includes a logarithmic convolution term and an external potential&nbsp; . There is a threshold&nbsp; &nbsp;that we establish existence and nonexist-ence results for constraint minimizers: for&nbsp; , minimizers exist for any&nbsp; ; for&nbsp; &nbsp;with&nbsp; &nbsp;and&nbsp; &nbsp;with&nbsp; , no minimizer exists. Furthermore, for&nbsp; &nbsp;and&nbsp; , we analyze the limiting behavior of positive minimizers, showing that after suitable scaling, they converge to the standard ground state solution&nbsp; &nbsp;of&nbsp; &nbsp;in&nbsp; . We also de-rive asymptotic estimates for the location of the maximum points of mini-mizers.<br />
%K Gross-Pitaevskii Functional
%K Constraint Minimizers
%K Logarithmic Convolution
%K Ringed Shape Potential
%U http://www.oalib.com/paper/6888068