Geodesic
Nodal solutions for scalar curvature type equations with perturbation terms on compact Riemannian manifolds
Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 1, pp. 205-226.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In this paper we study the nodal solutions for scalar curvature type equations with perturbation. The main results concern the existence of such solutions and the exact description of their zero set. From this we deduce, in particular cases, some multiplicity results.
L'oggetto del presente articolo è lo studio delle soluzioni soggette a cambiamenti di segno delle equazioni di tipo curvatura scalare a perturbazione. I principali risultati in esso contenuti riguardano l'esistenza di tali soluzioni e la determinazione puntuale del loro insieme degli zeri. Da ciò deduciamo, in alcuni casi, dei risultati di molteplicità. 
@article{BUMI_2002_8_5B_1_a9,
     author = {Djadli, Zindine and Jourdain, Antoinette},
     title = {Nodal solutions for scalar curvature type equations with perturbation terms on compact {Riemannian} manifolds},
     journal = {Bollettino della Unione matematica italiana},
     pages = {205--226},
     publisher = {mathdoc},
     volume = {Ser. 8, 5B},
     number = {1},
     year = {2002},
     zbl = {1177.58016},
     mrnumber = {370183},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_1_a9/}
}
TY  - JOUR
AU  - Djadli, Zindine
AU  - Jourdain, Antoinette
TI  - Nodal solutions for scalar curvature type equations with perturbation terms on compact Riemannian manifolds
JO  - Bollettino della Unione matematica italiana
PY  - 2002
SP  - 205
EP  - 226
VL  - 5B
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_1_a9/
LA  - en
ID  - BUMI_2002_8_5B_1_a9
ER  - 
%0 Journal Article
%A Djadli, Zindine
%A Jourdain, Antoinette
%T Nodal solutions for scalar curvature type equations with perturbation terms on compact Riemannian manifolds
%J Bollettino della Unione matematica italiana
%D 2002
%P 205-226
%V 5B
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_1_a9/
%G en
%F BUMI_2002_8_5B_1_a9
Djadli, Zindine; Jourdain, Antoinette. Nodal solutions for scalar curvature type equations with perturbation terms on compact Riemannian manifolds. Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 1, pp. 205-226. http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_1_a9/

[1] A. Ambrosetti-P. Rabinowitz, Dual variational methods in critical point theory and applications, Journal of Functional Analysis, 14 (1973), 349-381. | MR | Zbl

[2] F. V. Atkinson, H. Brézis - L. A. Peletier, Nodal solutions of elliptic equations with critical Sobolev exponents, Journal of Differential Equations, 85 (1990), 151-170. | MR | Zbl

[3] T. Aubin, Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire, Journal de Mathématiques Pures et Appliquées, 55 (1976), 269-296. | MR | Zbl

[4] H. Brézis-L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Communications on Pure and Applied Mathematics, 36 (1983), 437-477. | MR | Zbl

[5] H. Brézis-L. Nirenberg, Remarks on finding critical points, Communications on Pure and Applied Mathematics, 44 (1991), 939-963. | MR | Zbl

[6] D. Cao-E. S. Noussair, Multiple positive and nodal solutions for semilinear elliptic problems with critical exponents, Indiana University Mathematics Journal, 44 (1995), 1249-1271. | MR | Zbl

[7] F. Demengel-E. Hebey, On some nonlinear equations involving the $p$-laplacian with critical Sobolev growth and perturbation terms, to appear in Applicable Analysis. | MR | Zbl

[8] Z. Djadli, Equations de Yamabe perturbées, Thèse de l'Université de Cergy-Pontoise, 1998.

[9] Z. Djadli, Nonlinear elliptic equations with critical Sobolev exponent on compact riemannian manifolds, Calculus of Variations and Partial Differential Equations, 8 (1999), 293-326. | MR | Zbl

[10] D. Fortunato-E. Jannelli, Infinitely many solutions for some nonlinear elliptic problems in symmetrical domains, Proceedings of the Royal Society of Edinburgh Sect. A, 105 (1987), 205-213. | MR | Zbl

[11] E. Hebey, La méthode d'isométries concentration dans le cas d'un problème non linéaire sur les variétés compactes à bord avec exposant critique de Sobolev, Bulletin des Sciences Mathématiques, 116 (1992), 36-51. | MR | Zbl

[12] E. Hebey, Introduction à l'analyse non linéaire sur les variétés, Diderot Editions, Collection Fondations, 1997. | Zbl

[13] E. Hebey-M. Vaugon, Existence and multiplicity of nodal solutions for nonlinear elliptic equations with critical Sobolev growth, Journal of Functional Analysis, 119 (1994), 298-318. | MR | Zbl

[14] A. Jourdain, Solutions nodales pour des équations du type courbure scalaire sur la sphère, Bulletin des Sciences Mathématiques, 123 (1999), 299-327. | MR | Zbl

[15] J. L. Kazdan-F. W. Warner, Remarks on some quasilinear elliptic equations, Communications on Pure and Applied Mathematics, 28 (1975), 567-597. | MR | Zbl

[16] M. Musso-D. Passaseo, Sign changing solutions of nonlinear elliptic equations, Advances in Differential Equations, 1 (1996), 1025-1052. | MR | Zbl

[17] G. Tarantello, Nodal solutions of semilinear elliptic equations with critical exponent, Differential Integral Equations, 5 (1992), 25-42. | MR | Zbl

[18] N. Trudinger, Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Annali della Scuola Normale Superiore di Pisa, 22 (1968), 265-274. | fulltext mini-dml | MR | Zbl

[19] H. Yamabe, On a deformation of Riemannian structures on compact manifolds, Osaka Mathematical Journal, 12 (1960), 21-37. | fulltext mini-dml | MR | Zbl