Mixed Type Solutions of the Models on a Torus

作者：Fan Yen Wen^*; Lee Youngae^*; Lin Chang Shou^*

来源：Communications in Mathematical Physics, 2016, 343(1): 233-271.

DOI：10.1007/s00220-015-2532-4

In this paper, we study mixed-type solutions of Chern-Simons system (see (1.4) below) on a two dimensional flat torus. Nolasco and Tarantello (Commun Math Phys 213:599-639, 2000), among other things, Nolasco and Tarantello obtained solutions of (1.4) as minimizers of several functionals closely related to (1.4), and showed that if , then one of those minimizers turns out to be a mixed-type solution, that is, one component tends to pointwise a.e. and the other component converges to a solution of a mean field equation. We call these kinds of solutions mixed-type (I) solutions. In this paper, we prove two main results: (i) the asymptotic analysis of mixed-type (I) solutions with arbitrary configuration of vortex points, and (ii) the existence of mixed-type (I) solutions under a non-degenerate condition. This non-degenerate condition also ensures some uniqueness result. In particular, our results imply that when , there are only two mixed-type (I) solutions of (1.4).

• 出版日期2016-4