TY - JOUR
T1 - Bubbling solutions of mixed type for a general non-Abelian Chern–Simons–Higgs system of rank 2 over a torus
AU - Huang, Hsin Yuan
AU - Lee, Youngae
AU - Moon, Sang Hyuck
N1 - Publisher Copyright:
© 2021 Elsevier Ltd
PY - 2022/1
Y1 - 2022/1
N2 - We consider a general non-Abelian Chern–Simons–Higgs system of rank 2 [Formula presented] over a flat torus, where m1,l≥0, m2,l≥0, (m1,l,m2,l)≠(0,0) for l=1,…,N, δp is the Dirac measure at p, K is a non-degenerate 2 × 2 matrix of the form K=1+a−a−b1+b. When a>−1, b>−1, and a+b>−1, Eqs (0.1) are expected to have three types solutions: topological, non-topological and mixed type solutions. Concerning the existence of various type solutions, there are requirements that a>0 and b>0, or a and b are close to 0 in the literature. It is still open for generic a and b. We partially answer this question and show that (0.1) possesses bubbling mixed type solutions provided that ɛ is small and (a,b) satisfies (1.17).
AB - We consider a general non-Abelian Chern–Simons–Higgs system of rank 2 [Formula presented] over a flat torus, where m1,l≥0, m2,l≥0, (m1,l,m2,l)≠(0,0) for l=1,…,N, δp is the Dirac measure at p, K is a non-degenerate 2 × 2 matrix of the form K=1+a−a−b1+b. When a>−1, b>−1, and a+b>−1, Eqs (0.1) are expected to have three types solutions: topological, non-topological and mixed type solutions. Concerning the existence of various type solutions, there are requirements that a>0 and b>0, or a and b are close to 0 in the literature. It is still open for generic a and b. We partially answer this question and show that (0.1) possesses bubbling mixed type solutions provided that ɛ is small and (a,b) satisfies (1.17).
KW - Bubbling mixed type solutions
KW - Non-Abelian Chern–Simons models
UR - http://www.scopus.com/inward/record.url?scp=85113330475&partnerID=8YFLogxK
U2 - 10.1016/j.na.2021.112552
DO - 10.1016/j.na.2021.112552
M3 - Article
AN - SCOPUS:85113330475
SN - 0362-546X
VL - 214
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
M1 - 112552
ER -