Existence of non-topological solutions for a skew-symmetric Chern-Simons   system
  We investigate the existence of non-topological solutions $(u_1,u_2)$ satisfying   $$u_{i}(x)=-2\beta_i\ln|x|+O(1),\quad\text{as }|x|\rightarrow +\infty,$$ such that $\beta_i>1$ and   $$(\beta_1-1)(\beta_2-1)>(N_1+1)(N_2+1),$$   for a skew-symmetric Chern-Simons system. By the bubbling analysis and the Leray-Schauder degree theory, we get the existence results except for a finite set of curves: $$\frac{N_1}{\beta_1+N_1}+\frac{N_2}{\beta_2+N_2}=\frac{k-1}{k},k=2,\cdots,\max(N_1,N_2).$$ This generalizes a previous work by Choe-Kim-Lin \cite{ChoeKimLin2011}. 
Genggeng Huang and Chang-Shou Lin
math.AP