no. 5
Existence results for mean field equations
Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999) no. 5, pp. 653-666. 
@article{AIHPC_1999__16_5_653_0,
     author = {Ding, Weiyue and Jost, J\"urgen and Li, Jiayu and Wang, Guofang},
     title = {Existence results for mean field equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {653--666},
     publisher = {Gauthier-Villars},
     volume = {16},
     number = {5},
     year = {1999},
     mrnumber = {1712560},
     zbl = {0937.35055},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_1999__16_5_653_0/}
}
TY  - JOUR
AU  - Ding, Weiyue
AU  - Jost, Jürgen
AU  - Li, Jiayu
AU  - Wang, Guofang
TI  - Existence results for mean field equations
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1999
SP  - 653
EP  - 666
VL  - 16
IS  - 5
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPC_1999__16_5_653_0/
LA  - en
ID  - AIHPC_1999__16_5_653_0
ER  - 
%0 Journal Article
%A Ding, Weiyue
%A Jost, Jürgen
%A Li, Jiayu
%A Wang, Guofang
%T Existence results for mean field equations
%J Annales de l'I.H.P. Analyse non linéaire
%D 1999
%P 653-666
%V 16
%N 5
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPC_1999__16_5_653_0/
%G en
%F AIHPC_1999__16_5_653_0
Ding, Weiyue; Jost, Jürgen; Li, Jiayu; Wang, Guofang. Existence results for mean field equations. Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999) no. 5, pp. 653-666. http://archive.numdam.org/item/AIHPC_1999__16_5_653_0/

[1] T. Aubin, Nonlinear analysis on manifolds, Springer-Verlag, 1982. | MR | Zbl

[2] A. Bahri and J.M. Coron, Sur une equation elliptique non lineaire avec l'exposant critique de Sobolev, C. R. Acad. Sci. Paris Ser. I, Vol. 301, 1985, pp. 345-348. | MR | Zbl

[3] H. Brezis and F. Merle, Uniform estimates and blow up behavior for solutions of -Δu = V(x)eu in two dimensions, Comm. Partial Diff. Equat., Vol. 16, 1991, pp. 1223-1253. | MR | Zbl

[4] E.P. Caglioti, P.L. Lions, C. Marchioro and M. Pulvirenti, A special class of stationary flows for two-dimensional Euler equations: a statistical mechanics description, Commun. Math. Phys., Vol. 143, 1992, pp. 501-525. | MR | Zbl

[5] E. Caglioti, P.L. Lions, C. Marchioro and M. Pulvirenti, A special class of stationary flows for two-dimensional Euler equations: a statistical mechanics description. Part II, Commun. Math. Phys., Vol. 174, 1995, pp. 229-260. | MR | Zbl

[6] W.X. Chen and C. Li, Prescribing Gaussian curvature on surfaces with conical singularities, J. Geom. Anal., Vol. 1, 1991, pp. 359-372. | MR | Zbl

[7] W. Ding, J. Jost, J. Li and G. Wang, The differential equation Δu = 8π - 8πheu on a compact Riemann surface, Asian J. Math., Vol. 1, 1997, pp. 230-248. | MR | Zbl

[8] J. Kazdan and F. Warner, Curvature functions for compact 2-manifolds, Ann. Math., Vol. 99, 1974 , pp. 14-47. | MR | Zbl

[9] M.K.H. Kiessling, Statistical mechanics of classical particles with logarithmic interactions, Comm. Pure Appl. Math., Vol. 46, 1993, pp. 27-56. | MR | Zbl

[10] Yan Yan Li, -Δu = λ(Veu/∫MVeu- W) on Riemann surfaces, preprint,

[11] Yan Yan Li and I. Shafrir, Blow-up analysis for solutions of -Δu = Veu in dimension two, Indiana Univ. Math. J., Vol. 43, 1994, pp. 1255-1270. | MR | Zbl

[12] C. Marchioro and M. Pulvirenti, Mathematical theory of incompressible nonviscous fluids, Appl. Math. Sci., Vol. 96, Springer-Verlag, 1994. | MR | Zbl

[13] J. Moser, A sharp form of an inequality of N. Trudinger, Indiana Univ. Math. J., Vol. 20, 1971, pp. 1077-1092. | Zbl

[14] M. Nolasco and G. Tarantello, On a sharp Sobolev type inequality on two dimensional compact manifolds, preprint. | MR

[15] R.S. Palais, Critical point theory and the minimax principle, Global Analysis, Proc. Sympos. Pure Math., Vol. 15, 1968, pp. 185-212. | MR | Zbl

[16] M. Struwe, The evolution of harmonic mappings with free boundaries, Manuscr. Math., Vol. 70, 1991, pp. 373-384. | MR | Zbl

[17] M. Struwe, Multiple solutions to the Dirichlet problem for the equation of prescribed mean curvature , Analysis, et cetera, P. H. RABINOWITZ and E. ZEHNDER Eds., 1990, pp. 639-666. | MR | Zbl

[18] M. Struwe and G. Tarantello, On multivortex solutions in Chern-Simons gauge theory, preprint. | MR

[19] T. Suzuki, Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity, Ann. Inst. H. Poincaré, Anal. Non Lineaire, Vol. 9, 1992, pp. 367-398. | Numdam | MR | Zbl