COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v.16, no.4, pp.1315 - 1330
Abstract
We consider a quasi-linear elliptic equation with Dirac source terms arising in a generalized self-dual Chern-Simons-Higgs gauge theory. In this paper, we study doubly periodic vortices with arbitrary vortex con figuration. First of all, we show that under doubly periodic condition, there are only two types of solutions, topological and non-topological solutions as the coupling parameter goes to zero. Moreover, we succeed to construct non-topological solution with k bubbles where k is an element of N is any given number. To find a solution, we analyze the structure of quasi-linear elliptic equation carefully and apply the method developed in the recent work [16].