Existence and asymptotic behavior of solutions in the Chern-Simons O(3) sigma model

초록

In this talk an elliptic equation arising from the Chern-Simons O(3) sigma model is introduced.Unlike the well-known Chern-Simons Higgs vortex equation, this equation has both positive and negative singular sources. We prove multiple exitence results for doubly periodic solutions in the Chern-Simons O(3) sigma model by using the variational method as well as the super/subsolution method. Then we deal with asymptotic behavior of two different solutions. We also discuss how the negative singular sources influence asymptotic behavior of solutions. 2010 Mathematics Subject Classification: 81T13, 35B40