Djadli, Zindine and Jourdain, Antoinette:
Nodal solutions for scalar curvature type equations with perturbation terms on compact Riemannian manifolds
Bollettino dell'Unione Matematica Italiana Serie 8 5-B (2002), fasc. n.1, p. 205-226, Unione Matematica Italiana (English)
pdf (314 Kb), djvu (274 Kb). | MR1881932 | Zbl 1177.58016
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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.
Referenze Bibliografiche
[1]
A. AMBROSETTI-
P. RABINOWITZ,
Dual variational methods in critical point theory and applications,
Journal of Functional Analysis,
14 (
1973), 349-381. |
MR 370183 |
Zbl 0273.49063[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 1052332 |
Zbl 0702.35099[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 431287 |
Zbl 0336.53033[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 709644 |
Zbl 0541.35029[5]
H. BRÉZIS-
L. NIRENBERG,
Remarks on finding critical points,
Communications on Pure and Applied Mathematics,
44 (
1991), 939-963. |
MR 1127041 |
Zbl 0751.58006[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 1386768 |
Zbl 0849.35030[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 1775436 |
Zbl 1005.35047[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 1700267 |
Zbl 0953.58017[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 890056 |
Zbl 0676.35024[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 1154371 |
Zbl 0756.35028[12]
E. HEBEY,
Introduction à l'analyse non linéaire sur les variétés,
Diderot Editions,
Collection Fondations,
1997. |
Zbl 0918.58001[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 1261094 |
Zbl 0798.35052[14]
A. JOURDAIN,
Solutions nodales pour des équations du type courbure scalaire sur la sphère,
Bulletin des Sciences Mathématiques,
123 (
1999), 299-327. |
MR 1697459 |
Zbl 1126.53309[15]
J. L. KAZDAN-
F. W. WARNER,
Remarks on some quasilinear elliptic equations,
Communications on Pure and Applied Mathematics,
28 (
1975), 567-597. |
MR 477445 |
Zbl 0325.35038[16]
M. MUSSO-
D. PASSASEO,
Sign changing solutions of nonlinear elliptic equations,
Advances in Differential Equations,
1 (
1996), 1025-1052. |
MR 1409898 |
Zbl 0864.35044[17]
G. TARANTELLO,
Nodal solutions of semilinear elliptic equations with critical exponent,
Differential Integral Equations,
5 (
1992), 25-42. |
MR 1141725 |
Zbl 0758.35035[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 240748 |
Zbl 0159.23801
Con il contributo del Ministero per i Beni e le Attività Culturali