Abstract
In this paper, we investigate the existence of solutions for a system of BPS vortex equations arising from the theory of multiple intersecting D-branes. Using a direct minimization method, we establish a sharp existence and uniqueness theorem for this system over a doubly periodic domain and over the full plane, respectively. In particular, we obtain an explicit necessary and sufficient condition, explicitly expressed in terms of the vortex numbers and the size of the domain, for the existence of a solution of the system in the doubly periodic domain case.
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