Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents

Giovanna Cerami; Donato Fortunato; Michaël Struwe

Annales de l'I.H.P. Analyse non linéaire (1984)

  • Volume: 1, Issue: 5, page 341-350
  • ISSN: 0294-1449

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Cerami, Giovanna, Fortunato, Donato, and Struwe, Michaël. "Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents." Annales de l'I.H.P. Analyse non linéaire 1.5 (1984): 341-350. <http://eudml.org/doc/78079>.

@article{Cerami1984,
author = {Cerami, Giovanna, Fortunato, Donato, Struwe, Michaël},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Palais Smale condition; semilinear elliptic equation; critical points; multiplicity; critical Sobolev exponent; existence; Laplace-Beltrami},
language = {eng},
number = {5},
pages = {341-350},
publisher = {Gauthier-Villars},
title = {Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents},
url = {http://eudml.org/doc/78079},
volume = {1},
year = {1984},
}

TY - JOUR
AU - Cerami, Giovanna
AU - Fortunato, Donato
AU - Struwe, Michaël
TI - Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1984
PB - Gauthier-Villars
VL - 1
IS - 5
SP - 341
EP - 350
LA - eng
KW - Palais Smale condition; semilinear elliptic equation; critical points; multiplicity; critical Sobolev exponent; existence; Laplace-Beltrami
UR - http://eudml.org/doc/78079
ER -

References

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  1. [0] A. Ambrosetti, P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. funct. Anal., t. 14, 1973, p. 349-381. Zbl0273.49063MR370183
  2. [1] Th. Aubin, Problèmes isopérimétriques et espaces de Sobolev, J. Diff. Geom., t. 11, 1976, p. 573-598. Zbl0371.46011MR448404
  3. [2] Th. Aubin, Nonlinear analysis on manifolds, Monge-Ampere equations. Springer Grundelehren 252, 1982. Zbl0512.53044MR681859
  4. [3] P. Bartolo, V. Benci, D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with « strong resonance » at infinity, Journal of nonlinear Anal. T. M. A., t. 7, 1983, p. 981-1012. Zbl0522.58012MR713209
  5. [4] V. Benci, D. Fortunato, The dual method in critical point Theory. Multiplicity results for indefinite functionals, Ann. Mat. Pura Appl., t. 32, 1982, p. 215-242. Zbl0526.58013MR696044
  6. [5] H. Brezis, L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math., t. XXXVI, 1983. Zbl0541.35029MR709644
  7. [6] H. Brezis, T. Kato, Remarks on the Schrodinger operator with singular complex potential, J. Math. Pures et Appl., t. 58, 1979, p. 137-151. Zbl0408.35025MR539217
  8. [7] S. Luckhaus, Existence and regularity of weak solutions to the Dirichlet problem for semilinear elliptic systems of high order, J. Reine und Angew. Math., t. 306, 1979, p. 192-207. Zbl0395.35026MR524655
  9. [8] S.J. Pohozaev, Eigenfunctions of the equation Δu + λf(u) = 0, Soviet Math. Doklady, t. 6, 1965, p. 1408-1411 (Translated from the Russian Dokl. Akad. Nauk SSSR, t. 165, 1965, p. 33-36.) Zbl0141.30202MR192184
  10. [9] G. Talenti, Best constants in Sobolev inequality, Ann. Mat. Pure Appl., t. 110, 1976, p. 353-372. Zbl0353.46018MR463908
  11. [10] N. Trudinger, Remarks concerning the conformal deformation of Riemannian structure on compact manifolds, Ann. Sc. Norm. Sup. Pisa, t. 22, 1968, p. 265-274. Zbl0159.23801MR240748

Citations in EuDML Documents

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  1. D. Fortunato, G. Palmieri, Remarks on the Yamabe problem and the Palais-Smale condition
  2. A. Capozzi, D. Fortunato, G. Palmieri, An existence result for nonlinear elliptic problems involving critical Sobolev exponent
  3. David E. Edmunds, Donato Fortunato, Enrico Jannelli, Fourth-order nonlinear elliptic equations with critical growth
  4. David E. Edmunds, Donato Fortunato, Enrico Jannelli, Fourth-order nonlinear elliptic equations with critical growth
  5. Elves A. B. Silva, Magda S Xavier, Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents

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