On condensate of solutions for the Chern–Simons–Higgs equation
Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 5, pp. 1329-1354.

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.

DOI : 10.1016/j.anihpc.2016.10.006
Mots clés : Condensate, Chern–Simons–Higgs equation, Bubbling phenomena, Pohozaev identity, Uniqueness
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Lin, Chang-Shou; Yan, Shusen. On condensate of solutions for the Chern–Simons–Higgs equation. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 5, pp. 1329-1354. doi : 10.1016/j.anihpc.2016.10.006. http://www.numdam.org/articles/10.1016/j.anihpc.2016.10.006/

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