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

Lin, Chang-Shou; Yan, Shusen

doi:10.1016/j.anihpc.2016.10.006

Lin, Chang-Shou ; Yan, Shusen

Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 5, pp. 1329-1354.

Résumé

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.

MR Zbl

DOI : 10.1016/j.anihpc.2016.10.006

Mots clés : Condensate, Chern–Simons–Higgs equation, Bubbling phenomena, Pohozaev identity, Uniqueness

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     author = {Lin, Chang-Shou and Yan, Shusen},
     title = {On condensate of solutions for the {Chern{\textendash}Simons{\textendash}Higgs} equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1329--1354},
     publisher = {Elsevier},
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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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