Motivated by the analysis of the multiple bubbling phenomenon (Bartolucci et al. in Commun. Partial Differ. Equ. 29(7–8):1241–1265, 2004) for a singular mean field equation on the unit disk (Bartolucci and Montefusco in Nonlinearity 19:611–631, 2006), for any N≥3 we characterize a subset of the 2π/N-symmetric part of the critical set of the N-vortex singular Hamiltonian. In particular we prove that this critical subset is of saddle type. As a consequence of our result, and motivated by a recently posed open problem (Bartolucci et al. in Commun. Partial Differ. Equ. 29(7–8):1241–1265, 2004), we can prove the existence of a multiple bubbling sequence of solutions for the singular mean field equation.

Bartolucci, D. (2010). On the classification of N-point concentrating solutions for mean field equations and the critical set of the N-vortex singular Hamiltonian on the unit disk. ACTA APPLICANDAE MATHEMATICAE, 110, 1-22 [10.1007/s10440-008-9376-2].

On the classification of N-point concentrating solutions for mean field equations and the critical set of the N-vortex singular Hamiltonian on the unit disk

BARTOLUCCI, DANIELE
2010

Abstract

Motivated by the analysis of the multiple bubbling phenomenon (Bartolucci et al. in Commun. Partial Differ. Equ. 29(7–8):1241–1265, 2004) for a singular mean field equation on the unit disk (Bartolucci and Montefusco in Nonlinearity 19:611–631, 2006), for any N≥3 we characterize a subset of the 2π/N-symmetric part of the critical set of the N-vortex singular Hamiltonian. In particular we prove that this critical subset is of saddle type. As a consequence of our result, and motivated by a recently posed open problem (Bartolucci et al. in Commun. Partial Differ. Equ. 29(7–8):1241–1265, 2004), we can prove the existence of a multiple bubbling sequence of solutions for the singular mean field equation.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - Analisi Matematica
English
Con Impact Factor ISI
Bartolucci, D. (2010). On the classification of N-point concentrating solutions for mean field equations and the critical set of the N-vortex singular Hamiltonian on the unit disk. ACTA APPLICANDAE MATHEMATICAE, 110, 1-22 [10.1007/s10440-008-9376-2].
Bartolucci, D
Articolo su rivista
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/11811
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact