By considering an abelian Chern-Simons model, we are led to study the existence of solutions of the Liouville equation with singularities on a flat torus. A non-existence and degree counting for solutions are obtained. The former result has an application in the Chern-Simons model.
@article{ASNSP_2004_5_3_2_367_0, author = {Chen, Chiun-Chuan and Lin, Chang-Shou and Wang, Guofang}, title = {Concentration phenomena of two-vortex solutions in a Chern-Simons model}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {367--397}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 3}, number = {2}, year = {2004}, zbl = {1170.35413}, mrnumber = {2075988}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2004_5_3_2_367_0/} }
Chen, Chiun-Chuan; Lin, Chang-Shou; Wang, Guofang. Concentration phenomena of two-vortex solutions in a Chern-Simons model. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 2, pp. 367-397. http://www.numdam.org/item/ASNSP_2004_5_3_2_367_0/
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