Asymptotic behaviors of governing equation of gauged sigma model for Heisenberg ferromagnet

Abstract

In this note, we study weak solutions of equationare Dirac masses concentrated at the points p i , i = 1, · · · , N , (resp. q j , i = 1, · · · , M ) and N − M > 1. Here equation (0.1) presents a governing equation of Gauged Sigma model for Heisenberg ferromagnet and we prove that it has a sequence of solutions u β having behaviors as −2πβ ln |x| + O(1) at infinity with a free parameter β ∈ (2, 2(N − M )), and our concern in this paper is to study the asymptotic behavior's estimates in the extremal case that β near 2 and 2(N − M ).