Clustered solutions around harmonic centers to a coupled elliptic system
Teresa D'Aprile
Dipartimento di Matematica, via E. Orabona 4, 70125 Bari, ItalyJuncheng Wei
Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
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Abstract
We study the following system of Schrödinger–Maxwell equations
where is a smooth and bounded domain of . We prove that for any integer the system has a family of solutions such that the form of consists of spikes concentrating at a harmonic center of as . Furthermore we show that the spikes approach the vertexes of a configuration which maximizes a suitable geometrical problem.
Résumé
On étudie le système d'équations de Schrödinger–Maxwell suivant :
où est un ouvert borné régulier. On montre que pour tout entier le système a une famille de solutions telle que la forme de consiste en pointes qui se concentrent sur un centre harmonique de lorsque . On montre, en plus, que les pointes approchent les sommets d'une configuration qui maximise un problème géométrique.
Cite this article
Teresa D'Aprile, Juncheng Wei, Clustered solutions around harmonic centers to a coupled elliptic system. Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007), no. 4, pp. 605–628
DOI 10.1016/J.ANIHPC.2006.04.003