By Bartolucci D.
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Additional info for 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
Poincar´e Anal. Non Lin´eaire 22 227  Esposito P, Pistoia A and Wei J 2006 Concentrating solutions for the H´enon equation in R2 , Preprint  Eyink G L and Spohn H 1993 Negative temperature states and large-scale, long-lived vortices in two dimensional turbulence, J. Stat. Phys. 70 833  Henrici P 1974 Applied and Computational Complex Analysis, Vol I, John Wiley & Sons, New-York p. 700  Kiessling MHK 1993 Statistical mechanics of classical particles with logaritmic interaction Comm.
In this case PN (r; ρ, α) has one and only one root in (0, 1) but for ρ small enough may admit at least another zero r0 > 1. 9 Acknowledgments We would like to thank very much E. Caglioti for illuminating discussions concerning the N -vortex problem. In particular we are indebted with him for some crucial observations concerning the case α = 0. Those remarks has been very useful in the drawing up of the final version of this paper. N-Vortex concentrating solutions for the singular mean field equation 35  Bartolucci D, Caglioti E & Montefusco E, in preparation.
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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 by Bartolucci D.