VORTEX CONDENSATION IN GENERAL U(1)×U(1) ABELIAN CHERN-SIMONS MODEL ON A FLAT TORUS

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.