Asymptotic analysis of solutions to a gauged \( O\left(\right.3\left.\right) \) sigma model
Daniele Bartolucci, Youngae Lee, Chang‐Shou Lin, Michiaki Onodera · Annales de l Institut Henri Poincaré C Analyse Non Linéaire · 2014
We analyze an elliptic equation arising in the study of the gauged \mathrm{O}(3) sigma model with the Chern–Simons term. In this paper, we study the asymptotic behavior of solutions and apply it to prove the uniqueness of stable solutions. However, one of the features of this nonlinear equation is the existence of stable nontopological solutions in \mathbb{R}^{2} , which implies the possibility that a stable solution which blows up at a vortex point exists. To exclude this kind of blow up behavior is one of the main difficulties which we have to overcome.