Comptes Rendus
Partial Differential Equations
Classification of positive solutions of semilinear elliptic equations
[Classification des solutions positives d'une EDP semi-linéaire]
Comptes Rendus. Mathématique, Volume 338 (2004) no. 1, pp. 7-11.

Nous donnons une classification de toutes les solutions d'une EDP semi-linéaire générale dans le quadrant positif de 2 .

We give a classification of all solutions of a general semilinear PDE in the positive quadrant of 2 .

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2003.10.038
Jérôme Busca 1 ; Messoud Efendiev 2 ; S. Zelik 3

1 CNRS and Ceremade, Université Paris Dauphine, place Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France
2 Lehrstuhl für Analysis und Modellierung, Universität zu Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
3 CNRS and laboratoire de mathématiques, Université de Poitiers, SP2MI, téléport 2, boulevard Marie et Pierre Curie, BP 30179, 86962 Futuroscope cedex, France
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Jérôme Busca; Messoud Efendiev; S. Zelik. Classification of positive solutions of semilinear elliptic equations. Comptes Rendus. Mathématique, Volume 338 (2004) no. 1, pp. 7-11. doi : 10.1016/j.crma.2003.10.038. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.10.038/

[1] A. Babin; M. Vishik Attractors of Evolutionary Equations, Stud. Math. Appl., vol. 25, North-Holland, Amsterdam, 1992

[2] H. Berestycki; L. Caffarelli; L. Nirenberg Monotonicity for elliptic equations in unbounded Lipschitz domains, Comm. Pure Appl. Math., Volume 50 (1997) no. 11, pp. 1089-1111

[3] H. Berestycki; L. Caffarelli; L. Nirenberg Further quantitative properties for elliptic equations in unbounded domains, Ann. Scuola Norm Sup. Pisa Cl. Sci., Volume 25 (1998) no. 1–2, pp. 69-94

[4] H. Berestycki, M. Efendiev, S. Zelik, Dynamical approach for positive solutions of semilinear elliptic problems in unbounded domains, Preprint 01-11, Universitat Stuttgart, Mathematishes Institut, 2001

[5] H. Berestycki; P. Lions Nonlinear scalar field equations I. Existence of a ground state, Arch. Rational Mech. Anal., Volume 82 (1983), pp. 313-345

[6] J. Busca; P. Felmer Qualitative properties of some bounded positive solutions to scalar field equations, Calc. Var. Partial Differential Equations, Volume 13 (2001) no. 2, pp. 191-211

[7] J. Busca; B. Sirakov Symmetry results for semilinear elliptic systems in the whole space, J. Differential Equations, Volume 163 (2000) no. 1, pp. 41-56

[8] M. Esteban; P.-L. Lions Existence and non-existence results for semilinear elliptic problems in unbounded domains, Coll. Progress in PDE, Pitman Res. Notes, vol. 249, 1991, pp. 1-14

[9] B. Gidas; W. Ni; L. Nirenberg Symmetry and related properties via the maximum principle, Comm. Math. Phys., Volume 6 (1981), pp. 883-901

[10] B. Gidas; W. Ni; L. Nirenberg Symmetry of positive solutions of nonlinear elliptic equations in n , Math. Anal Appl. Part A, Academic Press, New York, 1981, pp. 369-402

[11] M. Kwong Uniqueness of positive solutions of Δuu+up=0 in n , Arch. Rational Mech. Anal., Volume 105 (1983), pp. 243-266

[12] R. Temam Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New-York, 1988

[13] A. Volpert; S. Khudyaev Analysis in Classes of Discontinuous Functions and Equations of Mathematical Physics, Nijhoff, Dordrecht, 1985

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