Geodesic
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 Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

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
Keywords: Condensate, Chern–Simons–Higgs equation, Bubbling phenomena, Pohozaev identity, Uniqueness 
@article{AIHPC_2017__34_5_1329_0,
     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},
     year = {2017},
     publisher = {Elsevier},
     volume = {34},
     number = {5},
     doi = {10.1016/j.anihpc.2016.10.006},
     zbl = {1387.35512},
     mrnumber = {3742527},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2016.10.006/}
}
TY  - JOUR
AU  - Lin, Chang-Shou
AU  - Yan, Shusen
TI  - On condensate of solutions for the Chern–Simons–Higgs equation
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2017
SP  - 1329
EP  - 1354
VL  - 34
IS  - 5
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2016.10.006/
DO  - 10.1016/j.anihpc.2016.10.006
LA  - en
ID  - AIHPC_2017__34_5_1329_0
ER  - 
%0 Journal Article
%A Lin, Chang-Shou
%A Yan, Shusen
%T On condensate of solutions for the Chern–Simons–Higgs equation
%J Annales de l'I.H.P. Analyse non linéaire
%D 2017
%P 1329-1354
%V 34
%N 5
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2016.10.006/
%R 10.1016/j.anihpc.2016.10.006
%G en
%F AIHPC_2017__34_5_1329_0
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

Cité par Sources :