Skip to main content

Variational methods in nonlinear problems

Part of the Lecture Notes in Mathematics book series (LNMCIME,volume 1365)

Keywords

  • Periodic Solution
  • Stationary Point
  • Hamiltonian System
  • Minimal Period
  • Critical Point Theory

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Ambrosetti, P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Func'l. Anal. 14 (1973), p. 349–381.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. A. Bahri, H. Berestycki. Existence of forced oscillations for some nonlinear differential equations, Comm. Pure Appl. Math. 37 (1984) p. 403–442.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. V. Benci. A geometrical index for the group S1 and some applications to the study of periodic solutions of ordinary differential equations, Comm. Pure Appl. Math. 34 (1981) p. 393–432.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. V. Benci, D. Fortunato. Un teorema di molteplicità per un' equazione ellittica nonlineare su varietà simmetriche, Metodi asintotici e topologici in problemi differenziali non lineari, Inst. Mat. Univ. dell'Aquila 1981. (Ed. L. Boccardo and A. M. Micheletti), Pitagora Ed. Bologna.

    Google Scholar 

  5. F. H. Clarke, I. Ekeland. Hamiltonian trajectories having prescribed minimal period, Comm. Pure Appl. Math. 33 (1980) p. 103–116.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. I. Ekeland. On the variational principle, J. Math. Anal. Appl. 47 (1974) p. 324–353.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. M. Girardi, M. Matzeu. Solutions of minimal period for a class of nonconvex Hamiltonian systems and application to the fixed energy problem, Nonlin. Anal. TMA 10 (1986) p. 371–382.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. L. Lyusternik, L. Schnirelman. Méthodes topologiques dans les problèmes variationnels, Hermann et Cie, Paris, 1934.

    Google Scholar 

  9. R. Michalek, Multiplicity results for differential equations with symmetry, Ph.D. Thesis, New York University, 1986.

    Google Scholar 

  10. R. Michalek, G. Tarantello. Subharmonic solutions with prescribed minimal period for nonautonomous Hamiltonian systems, J. Diff. Eq's., to appear.

    Google Scholar 

  11. L. Nirenberg. Variational and topological methods in nonlinear problems, Bull. Amer. Math. Soc. 4 (1981) p. 267–302.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. P. H. Rabinowitz. Variational methods for nonlinear eigenvalue problems, Eigenvalues of Nonlinear Problem (G. Prodi, Ed.) C.I.M.E. Ed. Cremonese, Roma, 1975, p. 141–195.

    Google Scholar 

  13. P. H. Rabinowitz. Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 31 (1978) p. 157–184.

    CrossRef  MathSciNet  Google Scholar 

  14. P. H. Rabinowitz. Minimax methods in critical point theory with applications to differential equations, Conf. Board of Math. Sci. Reg. Conf. Ser. in Math., No. 65, Amer. Math. Soc., 1986.

    Google Scholar 

  15. G. Tarantello. Subharmonic solutions for Hamiltonian systems via a ℤP-index theory, Submitted to Annali della Scuola Norm. Sup. di Pisa.

    Google Scholar 

  16. Z. Q. Wang. A ℤP-index theory; to appear.

    Google Scholar 

  17. Z. Q. Wang. A ℤP-Borsuk-Ulam theorem; to appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1989 Springer-Verlag

About this paper

Cite this paper

Nirenberg, L. (1989). Variational methods in nonlinear problems. In: Giaquinta, M. (eds) Topics in Calculus of Variations. Lecture Notes in Mathematics, vol 1365. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089179

Download citation

  • DOI: https://doi.org/10.1007/BFb0089179

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50727-7

  • Online ISBN: 978-3-540-46075-6

  • eBook Packages: Springer Book Archive