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Poincar´e Anal. Non Lin´eaire 22 227 [19] Esposito P, Pistoia A and Wei J 2006 Concentrating solutions for the H´enon equation in R2 , Preprint [20] 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 [21] Henrici P 1974 Applied and Computational Complex Analysis, Vol I, John Wiley & Sons, New-York p. 700 [22] 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 [1] Bartolucci D, Caglioti E & Montefusco E, in preparation.

H. Poincar´e Anal. Non Lin´eaire 18 271 [13] Chen CC and Lin CS 2002 Sharp Estimates for Solutions of Multi-bubbles in Compact Riemann Surfaces Comm. Pure Appl. Math. 55 728 [14] Chen CC and Lin CS 2003 Topological Degree for a Mean Field Equation on Riemann Surfaces Comm. Pure Appl. Math. 56 1667 [15] del Pino M, Kowalczyk M and Musso M 2005, Singular limits in Liouville-type equations, Calc. Var. Poincar`e Anal. , 16 653 [17] Djadli Z and Malchiodi A 2006 Existence result for the mean field problem on Riemann surfaces of all genus, Preprint [18] Esposito P, Grossi M and Pistoia A 2004 On the existence of blowing-up solutions for a mean field equation Ann.

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Numerische Mathematic Bd. 25 - 46

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