摘要
Let T^2 be a flat two-dimensional torus with fundamental cell domain [-1/2,1/2]×[-1/2,1/2],h（x） a positive smooth function satisfying the symmetric property （8） on T^2.In this paper we give some sufficient condition under which the mean field equation △u = 16π - 16πe^u, has a smooth solution.
Let T2 be a flat two-dimensional torus with fundamental cell domain [-21,21] × [-21,12],h(x) a positive smooth function satisfying the symmetric property(8) on T2. In this paper we give some suffcient condition under which the mean field equation u = 16π-16πheu,has a smooth solution.
基金
supported by National Natural Science Foundation of China (Grant No. 10701064, 10931001)
XINXING Project of Zhejiang University
