An existence theorem for a generalized self-dual Chern-Simons equation and its application

作者：Chen Shouxin^*; Han Xiaosen

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2013, 64(5): 1555-1570.

DOI：10.1007/s00033-013-0307-3

• Chern-Simons model
• Vortices
• Elliptic equation
• Constrained minimization

In this paper, we establish an existence theorem for a generalized self-dual Chern-Simons equation over a doubly periodic domain and use the existence theorem to prove the existence of doubly periodic self-dual vortices in a Maxwell-Chern-Simons model with non-minimal coupling. We find a necessary and sufficient condition for the existence of solutions of the generalized Chern-Simons equation. We prove the existence result by using two methods, a super- and sub-solution method and a constrained minimization method. Our main contribution is that we find a general inequality-type constraint by using the second method and it maybe applied to some related problems with the similar structures.

• 出版日期2013-10
• 单位河南大学