Analytical Issues in the Construction of Self-dual Chern–Simons Vortices

The asymptotic behavior of Chern–Simons Vortices for Gudnason Model

“…In order to obtain the existence result, they applied a minimization approach. For the recent developments of (1.1), we refer the readers to [15,19,20,23,30,35,37,38,44,53,61,73].…”

On the classification of solutions of cosmic strings equation

“…Apart from the existence result of (1.1), Tarantello in [26] studied the blow up behavior of the bubbling solution of (1.1) in R 2 . For the related work, we refer the readers to [2][3][4]15,21,22,27] and references therein. The purpose of this paper is to consider the stable solutions of this problem, which can be seen as the continuation of the work of Dancer-Farina [7] on Liouville equation and Wang-Ye [28] on Hénon-type elliptic equation.…”

“…27) for all |y| > 8R 0 and R = |y| 4 . Applying Lemma 2.4 with δ = C in the above estimate, one hasw(y) ≤ C R − N 2 w L 2 (B(y,2R)) ≤ C R − N L 2 (B(y,2R)) = o R − N +αas |y| → ∞ by(2.25).…”