Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772437 | Journal of Functional Analysis | 2017 | 43 Pages |
Abstract
We establish the existence of bubbling solutions for the following skew-symmetric Chern-Simons system{Îu1+1ε2eu2(1âeu1)=4Ïâi=1N1δpi1Îu2+1ε2eu1(1âeu2)=4Ïâi=1N2δpi2 over a parallelogram Ω with doubly periodic boundary condition, where ε>0 is a coupling parameter, and δp denotes the Dirac measure concentrated at p. We obtain that if (N1â1)(N2â1)>1, there exists an ε0>0 such that, for any εâ(0,ε0), the above system admits a solution (u1,ε,u2,ε) satisfying u1,ε and u2,ε blow up simultaneously at the point pâ, and1ε2euj,ε(1âeui,ε)â4ÏNiδpâ,1â¤i,jâ¤2,iâ j as εâ0, where the location of the point pâ defined by (1.12) satisfies the condition (1.13).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Xiaosen Han, Hsin-Yuan Huang, Chang-Shou Lin,