Existence and non-existence of solutions of the mean field equations on flat tori
Journal
Proceedings of the American Mathematical Society
Journal Volume
145
Journal Issue
9
Pages
3989-3996
Date Issued
2017
Author(s)
Abstract
We prove the existence or non-existence of solutions of the mean field equation (1.1) with n = 1 or n = 2 for a rectangular torus E. It is interesting to see that the results depend on the location of the half period (Formula Presented.).
Type
journal article