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.
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Bartolucci, D. On the Classification of N-Points Concentrating Solutions for Mean Field Equations and the Symmetry Properties of the N-Vortex Singular Hamiltonian on the Unit Disk. Acta Appl Math 110, 1–22 (2010). https://doi.org/10.1007/s10440-008-9376-2
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DOI: https://doi.org/10.1007/s10440-008-9376-2