TY - JOUR
T1 - VORTEX CONDENSATION IN GENERAL U(1)×U(1) ABELIAN CHERN-SIMONS MODEL ON A FLAT TORUS
AU - Huang, Hsin Yuan
N1 - Publisher Copyright:
© 2022 American Institute of Mathematical Sciences. All rights reserved.
PY - 2022/8
Y1 - 2022/8
N2 - In this paper, we study an elliptic system arising from the U(1)×U(1) Abelian Chern-Simons Model[25, 37] of the form (Formula presented) (1) which are defined on a parallelogram Ω in R2 with doubly periodic boundary conditions. Here, a and b are interaction constants, λ > 0 is related to coupling constant, mj > 0(j = 1, · · ·, k1), nj > 0(j = 1, · · ·, k2), δp is the Dirac measure, p is called vortex point. Concerning the existence results of this system over Ω, only the cases (a, b) = (0, 1)[28] and a > b > 0[14] were studied in the literature. The solvability of this system (1) is still an open problem as regards other parameters (a, b). We show that the system (1) admits topological solutions provided λ is large and b > a > 0 Our arguments are based on a iteration scheme and variational formulation.
AB - In this paper, we study an elliptic system arising from the U(1)×U(1) Abelian Chern-Simons Model[25, 37] of the form (Formula presented) (1) which are defined on a parallelogram Ω in R2 with doubly periodic boundary conditions. Here, a and b are interaction constants, λ > 0 is related to coupling constant, mj > 0(j = 1, · · ·, k1), nj > 0(j = 1, · · ·, k2), δp is the Dirac measure, p is called vortex point. Concerning the existence results of this system over Ω, only the cases (a, b) = (0, 1)[28] and a > b > 0[14] were studied in the literature. The solvability of this system (1) is still an open problem as regards other parameters (a, b). We show that the system (1) admits topological solutions provided λ is large and b > a > 0 Our arguments are based on a iteration scheme and variational formulation.
KW - Chern-Simons model
KW - super-sub solution method
KW - topological solutions
KW - variational method
UR - http://www.scopus.com/inward/record.url?scp=85134607945&partnerID=8YFLogxK
U2 - 10.3934/dcdsb.2021234
DO - 10.3934/dcdsb.2021234
M3 - Article
AN - SCOPUS:85134607945
SN - 1531-3492
VL - 27
SP - 4415
EP - 4428
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
IS - 8
ER -