On the Spectrum of a Nonlinear Planar Problem
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 1, pp. 191-222. 
@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},
     pages = {191--222},
     publisher = {Elsevier},
     volume = {26},
     number = {1},
     year = {2009},
     doi = {10.1016/j.anihpc.2007.10.004},
     mrnumber = {2483819},
     zbl = {1166.35028},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2007.10.004/}
}
TY  - JOUR
AU  - Gladiali, Francesca
AU  - Grossi, Massimo
TI  - On the Spectrum of a Nonlinear Planar Problem
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 191
EP  - 222
VL  - 26
IS  - 1
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2007.10.004/
DO  - 10.1016/j.anihpc.2007.10.004
LA  - en
ID  - AIHPC_2009__26_1_191_0
ER  - 
%0 Journal Article
%A Gladiali, Francesca
%A Grossi, Massimo
%T On the Spectrum of a Nonlinear Planar Problem
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 191-222
%V 26
%N 1
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2007.10.004/
%R 10.1016/j.anihpc.2007.10.004
%G en
%F 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) no. 1, pp. 191-222. doi : 10.1016/j.anihpc.2007.10.004. http://www.numdam.org/articles/10.1016/j.anihpc.2007.10.004/

[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 | Zbl

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

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

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

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

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

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

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

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

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

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

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

[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 | Zbl

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

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

[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 | Zbl

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

Cité par Sources :