Skip to main content
Log in

Elliptic equations with critical exponent on spherical caps of S3

  • Published:
Journal d’Analyse Mathématique Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. A. Ambrosetti, A. Malchiodi and W.-M. Ni,Singularly perturbated elliptic equations with symmetry: Existence of solutions concentrating on spheres. I, Comm. Math. Phys.235 (2003), 427–466.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Ambrosetti, A. Malchiodi and W-M. Ni,Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres. II, Indiana Univ. Math. J.53 (2004), 297–329.

    Article  MATH  MathSciNet  Google Scholar 

  3. C. Bandle, and R. Benguria,The Brezis-Nirenberg problem on S 3, J. Differential Equations178 (2002), 264–279.

    Article  MATH  MathSciNet  Google Scholar 

  4. C. Bandle and L. A. Peletier,Best constants and Emden equations for the critical exponent in S 3, Math. Ann.313 (1999), 83–93.

    Article  MATH  MathSciNet  Google Scholar 

  5. H. Brezis and Y. Y. Li,Some nonlinear elliptic equations have only constant solutions, 2005, Preprint.

  6. H. Brezis and L. Nirenberg,Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents Comm. Pure Appl. Math.36 (1983), 437–477.

    Article  MATH  MathSciNet  Google Scholar 

  7. H. Brezis and L. A. Peletier,Elliptic equations with critical exponents on S 3;new non-minimising solutions, C.R. Acad. Sci. Paris Ser. I339 (2004), 391–394.

    MATH  MathSciNet  Google Scholar 

  8. H. Brezis and L. A. Peletier,Preliminary Note, 2005.

  9. W. Chen and J. Wei,On Brezis-Nirenberg problem on S 3 and a conjecture of Bandle-Benguria, C. R. Acad. Sci. Paris, Ser. I,341 (2005), 153–156.

    MATH  MathSciNet  Google Scholar 

  10. J.-M. Coron,Topologie et cas limite des injections de Sobolev, C.R. Acad. Sci. Paris, Ser. I299 (1984), 209–212.

    MATH  MathSciNet  Google Scholar 

  11. M. Crandall and P. H. Rabinowitz,Bifurcation from simple eigenvalues, J. Funct. Anal.8 (1971), 321–340.

    Article  MATH  MathSciNet  Google Scholar 

  12. B. Gidas, W.-M. Ni and L. Nirenberg,Symmetry and related properties via the maximum principle, Comm. Math. Phys.68 (1979), 209–243.

    Article  MATH  MathSciNet  Google Scholar 

  13. B. Gidas and J. Spruck,Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math.34 (1981), 525–598.

    Article  MATH  MathSciNet  Google Scholar 

  14. C. Gui, J. Wei and M. Winter,Multiple boundary peak solutions for some singularly perturbed Neumann problems, Ann. Inst. H. Poincaré Anal. Non Linéaire17 (2000), 47–82.

    Article  MATH  MathSciNet  Google Scholar 

  15. M. K. Kwong and Y. Li,Uniqueness of radial solutions of semilinear elliptic equations, Trans. Amer. Math. Soc.333 (1992), 339–363.

    Article  MATH  MathSciNet  Google Scholar 

  16. A. Malchiodi, W.-M. Ni and J. Wei,Multiple clustered layer solutions for semilinear Neumann problems on a ball, Ann. Inst. H. Poincaré Anal. Non Linéaire22 (2005), 143–163.

    Article  MATH  MathSciNet  Google Scholar 

  17. P. Padilla,Symmetry properties of positive solutions of elliptic equations on symmetric domains, Appl. Anal.64, (1997), 153–169.

    Article  MATH  MathSciNet  Google Scholar 

  18. L. A. Peletier and W. C. Troy,Chaotic spatial patterns described by the Extended Fisher-Kolmogorov equation, J. Differential Equations126 (1996), 458–508.

    Article  MathSciNet  Google Scholar 

  19. L. A. Peletier and W. C. Troy,Spatial Patterns: Higher Order Models in Physics and Mechanics Birkhäuser, Boston, 2001.

    MATH  Google Scholar 

  20. S. I. Pohozaev,Eigenfunctions of the equation Δuf(u)=0, Dokl. Akad. Nauk165 (1965), 36–39 (in Russian) and Sov. Math.6 (1965), 1408–1411.

    MathSciNet  Google Scholar 

  21. S. I. Stingelin,Das Brezis-Nirenberg-Problem auf der Sphäre S n, Inauguraldissertation, Universität Basel, 2004. (Can be found under http://pages.unibas.ch/diss/2004/DissB_6814.htm.)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to H. Brezis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brezis, H., Peletier, L.A. Elliptic equations with critical exponent on spherical caps of S3 . J. Anal. Math. 98, 279–316 (2006). https://doi.org/10.1007/BF02790278

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02790278

Keywords

Navigation