Skip to main content
Springer Nature Link
Log in

Subharmonics of a Nonconvex Noncoercive Hamiltonian System

  • Published:
Ukrainian Mathematical Journal Aims and scope

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

We study the problem of the existence of multiple periodic solutions of the Hamiltonian system

$$J\dot x + u\nabla G\left( {t,u\left( x \right)} \right) = e\left( t \right),$$

where u is a linear mapping, G is a C 1-function, and e is a continuous function.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. C. Conley and E. Zehnder, “Subharmonic solutions and Morse theory,” Physica A, 124, 649–658 (1984).

    Google Scholar 

  2. I. Ekeland and H. Hofer, “Subharmonics for convex nonautonomous Hamiltonian systems,” Commun. Pure Appl. Math., 40, 1–36 (1987).

    Google Scholar 

  3. P. H. Rabinowitz, “On subharmonic solutions of Hamiltonian systems,” Commun. Pure Appl. Math., 33, 609–633 (1980).

    Google Scholar 

  4. M. Timoumi, “Subharmonics of convex noncoercive Hamiltonian systems,” Coll. Math., Fasc. 1, 63–69 (1992).

    Google Scholar 

  5. G. Fournier, M. Timoumi, and M. Willem, “The limiting case for strongly indefinite functionals,” Top. Meth. Nonlin. Anal., 1, 203–209 (1993).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Preparatory Institute of Engineering Studies, Tunisia

    N. Kallel & M. Timoumi

Authors
  1. N. Kallel
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. M. Timoumi
    View author publications

    You can also search for this author inPubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kallel, N., Timoumi, M. Subharmonics of a Nonconvex Noncoercive Hamiltonian System. Ukrainian Mathematical Journal 55, 1754–1764 (2003). https://doi.org/10.1023/B:UKMA.0000027040.19459.a4

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:UKMA.0000027040.19459.a4

Keywords