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

VL - 214

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

M1 - 112552

ER -