ArticleOriginal scientific text
Title
A geometric and analytic approach to some problems associated with Emden equations
Authors 1
Affiliations
- Département de Mathématiques, Faculté des Sciences, Parc de Grandmont, F-37200 Tours, France
Bibliography
- T. Aubin, Problèmes isopérimétriques et espaces de Sobolev, J. Differential Geom. 11 (1976), 573-598.
- M. Berger, P. Gauduchon et E. Mazet, Le spectre d'une variété riemannienne, Lecture Notes in Math. 194, Springer, 1971.
- M. F. Bidaut-Véron and L. Véron, Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations, Invent. Math. 106 (1991), 489-539.
- L. A. Caffarelli, B. Gidas and J. Spruck, Asymptotic symmetry and local behaviour of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42 (1989), 271-297.
- S. Chandrasekhar, An Introduction to the Study of Stellar Structure, Dover, 1967.
- S. Y. A. Chang and P. C. Yang, Prescribing Gaussian curvature on S², Acta Math. 159 (1987), 215-259.
- V. R. Emden, Gaskugeln, Teubner, Leipzig 1897.
- R. H. Fowler, Further studies of Emden's and similar differential equations, Quart. J. Math. Oxford Ser. 2 (1931), 259-288.
- B. Gidas and J. Spruck, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math. 34 (1981), 525-598.
- H. Hamza and S. Ilias, private communication and detailed paper, to appear.
- M. Obata, The conjectures on conformal transformations of Riemannian manifolds, J. Differential Geom. 6 (1971), 247-258.
- P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conf. Ser. in Math. 65, Amer. Math. Soc., 1984.
- L. Simon, Asymptotics for a class of nonlinear evolution equations with applications to geometric problems, Ann. of Math. 118 (1983), 525-571.
- L. Simon, Isolated singularities of extrema of geometric variational problems, in: Harmonic Mappings and Minimal Immersions, Lecture Notes in Math. 1161, Springer, 1985, 206-277.
- L. Simon, Entire solutions of the minimal surface equation, J. Differential Geom. 30 (1989), 643-688.