Nodal solutions for scalar curvature type equations with perturbation terms on compact Riemannian manifolds

Zindine Djadli; Antoinette Jourdain

Bollettino dell'Unione Matematica Italiana (2002)

  • Volume: 5-B, Issue: 1, page 205-226
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Djadli, Zindine, and Jourdain, Antoinette. "Nodal solutions for scalar curvature type equations with perturbation terms on compact Riemannian manifolds." Bollettino dell'Unione Matematica Italiana 5-B.1 (2002): 205-226. <http://eudml.org/doc/194568>.

@article{Djadli2002,
abstract = {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.},
author = {Djadli, Zindine, Jourdain, Antoinette},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {205-226},
publisher = {Unione Matematica Italiana},
title = {Nodal solutions for scalar curvature type equations with perturbation terms on compact Riemannian manifolds},
url = {http://eudml.org/doc/194568},
volume = {5-B},
year = {2002},
}

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 dell'Unione Matematica Italiana
DA - 2002/2//
PB - Unione Matematica Italiana
VL - 5-B
IS - 1
SP - 205
EP - 226
AB - 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.
LA - eng
UR - http://eudml.org/doc/194568
ER -

References

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  1. AMBROSETTI, A.- RABINOWITZ, P., Dual variational methods in critical point theory and applications, Journal of Functional Analysis, 14 (1973), 349-381. Zbl0273.49063MR370183
  2. ATKINSON, F. V., BRÉZIS, H. - PELETIER, L. A., Nodal solutions of elliptic equations with critical Sobolev exponents, Journal of Differential Equations, 85 (1990), 151-170. Zbl0702.35099MR1052332
  3. AUBIN, T., Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire, Journal de Mathématiques Pures et Appliquées, 55 (1976), 269-296. Zbl0336.53033MR431287
  4. BRÉZIS, H.- NIRENBERG, L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Communications on Pure and Applied Mathematics, 36 (1983), 437-477. Zbl0541.35029MR709644
  5. BRÉZIS, H.- NIRENBERG, L., Remarks on finding critical points, Communications on Pure and Applied Mathematics, 44 (1991), 939-963. Zbl0751.58006MR1127041
  6. CAO, D.- NOUSSAIR, E. S., Multiple positive and nodal solutions for semilinear elliptic problems with critical exponents, Indiana University Mathematics Journal, 44 (1995), 1249-1271. Zbl0849.35030MR1386768
  7. DEMENGEL, F.- HEBEY, E., On some nonlinear equations involving the p -laplacian with critical Sobolev growth and perturbation terms, to appear in Applicable Analysis. Zbl1005.35047MR1775436
  8. DJADLI, Z., Equations de Yamabe perturbées, Thèse de l'Université de Cergy-Pontoise, 1998. 
  9. DJADLI, Z., Nonlinear elliptic equations with critical Sobolev exponent on compact riemannian manifolds, Calculus of Variations and Partial Differential Equations, 8 (1999), 293-326. Zbl0953.58017MR1700267
  10. FORTUNATO, D.- JANNELLI, E., Infinitely many solutions for some nonlinear elliptic problems in symmetrical domains, Proceedings of the Royal Society of Edinburgh Sect. A, 105 (1987), 205-213. Zbl0676.35024MR890056
  11. HEBEY, E., 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. Zbl0756.35028MR1154371
  12. HEBEY, E., Introduction à l'analyse non linéaire sur les variétés, Diderot Editions, Collection Fondations, 1997. Zbl0918.58001
  13. HEBEY, E.- VAUGON, M., Existence and multiplicity of nodal solutions for nonlinear elliptic equations with critical Sobolev growth, Journal of Functional Analysis, 119 (1994), 298-318. Zbl0798.35052MR1261094
  14. JOURDAIN, A., Solutions nodales pour des équations du type courbure scalaire sur la sphère, Bulletin des Sciences Mathématiques, 123 (1999), 299-327. Zbl1126.53309MR1697459
  15. KAZDAN, J. L.- WARNER, F. W., Remarks on some quasilinear elliptic equations, Communications on Pure and Applied Mathematics, 28 (1975), 567-597. Zbl0325.35038MR477445
  16. MUSSO, M.- PASSASEO, D., Sign changing solutions of nonlinear elliptic equations, Advances in Differential Equations, 1 (1996), 1025-1052. Zbl0864.35044MR1409898
  17. TARANTELLO, G., Nodal solutions of semilinear elliptic equations with critical exponent, Differential Integral Equations, 5 (1992), 25-42. Zbl0758.35035MR1141725
  18. TRUDINGER, N., Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Annali della Scuola Normale Superiore di Pisa, 22 (1968), 265-274. Zbl0159.23801MR240748
  19. YAMABE, H., On a deformation of Riemannian structures on compact manifolds, Osaka Mathematical Journal, 12 (1960), 21-37. Zbl0096.37201MR125546

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