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