On the Spectrum of a Nonlinear Planar Problem
Gladiali, Francesca ; Grossi, Massimo
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009), p. 191-222 / Harvested from Numdam
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@article{AIHPC_2009__26_1_191_0,
     author = {Gladiali, Francesca and Grossi, Massimo},
     title = {On the Spectrum of a Nonlinear Planar Problem},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {26},
     year = {2009},
     pages = {191-222},
     doi = {10.1016/j.anihpc.2007.10.004},
     mrnumber = {2483819},
     zbl = {1166.35028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2009__26_1_191_0}
}

Gladiali, Francesca; Grossi, Massimo. On the Spectrum of a Nonlinear Planar Problem. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) pp. 191-222. doi : 10.1016/j.anihpc.2007.10.004. http://gdmltest.u-ga.fr/item/AIHPC_2009__26_1_191_0/

[1] Bahri A., Li Y., Rey O., On a Variational Problem With Lack of Compactness: the Topological Effect of the Critical Points at Infinity, Calc. Var. 3 (1995) 67-93. | MR 1384837 | Zbl 0814.35032

[2] Bandle C., Isoperimetric Inequalities and Applications, Pitman, Boston, 1980. | MR 572958 | Zbl 0436.35063

[3] Berestycki H., Niremberg L., Varadhan R. S., The Principal Eigenvalue and Maximum Principle for Second Order Elliptic Operators in General Domains, Comm. Pure Appl. Math 47 (1994) 47-92. | MR 1258192 | Zbl 0806.35129

[4] Caffarelli L. A., Friedman A., Convexity of Solutions of Semilinear Elliptic Equations, Duke Math. J. 52 (1985) 431-456. | MR 792181 | Zbl 0599.35065

[5] Caglioti E., Lions P. L., Marchioro C., Pulvirenti M., A Special Class of Stationary Flows for Two-Dimensional Euler Equations: a Statistical Mechanics Description, Part II, Commun. Math. Phys. 174 (1995) 229-260. | MR 1362165 | Zbl 0840.76002

[6] Caglioti E., Lions P. L., Marchioro C., Pulvirenti M., A Special Class of Stationary Flows for Two-Dimensional Euler Equations: a Statistical Mechanics Description, Commun. Math. Phys. 143 (1992) 501-525. | MR 1145596 | Zbl 0745.76001

[7] Carrier G. F., Pearson C. E., Partial Differential Equations, Academic Press, Inc., 1988. | MR 952148 | Zbl 0671.35001

[8] S.Y.A. Chang, C.C. Chen, C.S. Lin, Extremal functions for a mean field equation in two dimension, preprint. | MR 2055839

[9] Chanillo S., Kiessling M. H.K., Rotational Symmetry of Solutions of Some Nonlinear Problems in Statistical Mechanics and in Geometry, Comm. Math. Phys. 160 (2) (1994) 217-238. | MR 1262195 | Zbl 0821.35044

[10] Chen W., Li C., Classification of Solutions of Some Nonlinear Elliptic Equations, Duke Math. J. 63 (1991) 615-622. | MR 1121147 | Zbl 0768.35025

[11] Chen C. C., Lin C. S., On the Symmetry of Blowup Solutions to a Mean Field Equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (2001) 271-296. | Numdam | MR 1831657 | Zbl 0995.35004

[12] Ding W., Jost J., Li J., Wang G., Existence Results for Mean Field Equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999) 653-666. | Numdam | MR 1712560 | Zbl 0937.35055

[13] K. El Mehdi, M. Grossi, Asymptotic estimates and qualitative properties of an elliptic problem in dimension two, preprint. | MR 2033557

[14] Gilbarg D., Trudinger N. S., Elliptic Partial Differential Equations of Second Order, Springer, 1998. | Zbl 1042.35002

[15] Gladiali F., Grossi M., Some Results for the Gelfand's Problem, Comm. Partial Differential Equations 29 (9-10) (2004) 1335-1364. | MR 2103839 | Zbl 1140.35417

[16] Grossi M., Pacella F., On an Eigenvalue Problem Related to the Critical Exponent, Math. Z. 250 (1) (2005) 225-256. | MR 2136650 | Zbl 1122.35087

[17] Kiessling M. H.K., Statistical Mechanics of Classical Particles With Logarithmic Interactions, Comm. Pure Appl. Math. 46 (1) (1993) 27-56. | MR 1193342 | Zbl 0811.76002

[18] Li Y. Y., Harnack Type Inequality: the Method of Moving Planes, Commun. Math. Phys. 200 (1999) 421-444. | MR 1673972 | Zbl 0928.35057

[19] Melas A. D., On the Nodal Line of the Second Eigenfunction of the Laplacian in R 2 , J. Differential Geometry 35 (1992) 255-263. | MR 1152231 | Zbl 0769.58056

[20] Nagasaki K., Suzuki T., Asymptotic Analysis for Two-Dimensional Elliptic Eigenvalues Problems With Exponentially Dominated Nonlinearities, Asymptotic Anal. 3 (1990) 173-188. | MR 1061665 | Zbl 0726.35011

[21] Protter M. H., Weinberger H. F., Maximum Principles in Differential Equations, Prentice-Hall, New Jersey, 1967. | MR 219861 | Zbl 0153.13602

[22] Suzuki T., Global Analysis for a Two-Dimensional Eigenvalue Problem With Exponential Nonlinearity, Ann. Inst. H. Poincaré Anal. Non Linéaire 9 (1992) 367-398. | Numdam | MR 1186683 | Zbl 0785.35045

[23] Tarantello G., Multiple Condensate Solutions for the Chern-Simons-Higgs Theory, J. Math. Phys. 37 (1996) 3769-3796. | MR 1400816 | Zbl 0863.58081