On condensate of solutions for the Chern–Simons–Higgs equation

  • Chang-Shou Lin

    Taida Institute of Mathematical Sciences, Center for Advanced Study, National Taiwan University, Taipei 106, Taiwan
  • Shusen Yan

    Department of Mathematics, The University of New England, Armidale, NSW 2351, Australia


This is the first part of our comprehensive study on the structure of doubly periodic solutions for the Chern–Simons–Higgs equation with a small coupling constant. We first classify the bubbling type of the blow-up point according to the limit equations. Assuming that all the blow-up points are away from the vortex points, we prove the non-coexistence of different bubbling types in a sequence of bubbling solutions. Secondly, for the CS type bubbling solutions, we obtain an existence result without the condition on the blow-up set as in [4]. This seems to be the first general existence result of the multi-bubbling CS type solutions which is obtained under nearly necessary conditions. Necessary and sufficient conditions are also discussed for the existence of bubbling solutions blowing up at vortex points.

Cite this article

Chang-Shou Lin, Shusen Yan, On condensate of solutions for the Chern–Simons–Higgs equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 5, pp. 1329–1354

DOI 10.1016/J.ANIHPC.2016.10.006