Existence of self-dual non-topological solutions in the Chern–Simons Higgs model
Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 6, pp. 837-852.

Lʼobjectif de cet article est de prouver lʼexistence de solutions non-topologiques du modèle de Chern–Simons Higgs dans 2 . Un problème de longue date existe pour cette équation : Soit N points vortex et β>8π(N+1), existe-t-il une solution non-topologique dans 2 telle que le flux magnétique total est égal à β/2 ? Dans cet article, nous prouvons lʼexistence dʼune solution pour β{8πNk k-1|k=2,,N}. Nous appliquons lʼanalyse par bulles et la theorie de Leray–Schauder pour résoudre ce problème.

In this paper we investigate the existence of non-topological solutions of the Chern–Simons Higgs model in 2 . A long standing problem for this equation is: Given N vortex points and β>8π(N+1), does there exist a non-topological solution in 2 such that the total magnetic flux is equal to β/2? In this paper, we prove the existence of such a solution if β{8πNk k-1|k=2,,N}. We apply the bubbling analysis and the Leray–Schauder degree theory to solve this problem.

DOI : 10.1016/j.anihpc.2011.06.003
Mots clés : Semi-linear PDE, Non-topological vortices, Chern–Simons Higgs model
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Choe, Kwangseok; Kim, Namkwon; Lin, Chang-Shou. Existence of self-dual non-topological solutions in the Chern–Simons Higgs model. Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 6, pp. 837-852. doi : 10.1016/j.anihpc.2011.06.003. http://www.numdam.org/articles/10.1016/j.anihpc.2011.06.003/

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