Skip to main content
Advances in Continuous and Discrete Models

Theory and Modern Applications

Download PDF
  • Research Article
  • Open access
  • Published:

Multiple Periodic Solutions to Nonlinear Discrete Hamiltonian Systems

Advances in Difference Equations volume 2007, Article number: 041830 (2007) Cite this article

Abstract

An existence result of multiple periodic solutions to the asymptotically linear discrete Hamiltonian systems is obtained by using the Morse index theory.

[12345678910111213141516]

References

  1. Chang K-C: Infinite-Dimensional Morse Theory and Multiple Solution Problems, Progress in Nonlinear Differential Equations and Their Applications. Volume 6. Birkhäuser, Boston, Mass, USA; 1993.

    Book  Google Scholar 

  2. Ekeland I: Convexity Methods in Hamiltonian Mechanics, Results in Mathematics and Related Areas (3). Volume 19. Springer, Berlin, Germany; 1990.

    Book  Google Scholar 

  3. Long Y: Index Theory for Symplectic Paths with Applications, Progress in Mathematics. Volume 207. Birkhäuser, Basel, Switzerland; 2002.

    Book  Google Scholar 

  4. Mawhin J, Willem M: Critical Point Theory and Hamiltonian Systems, Applied Mathematical Sciences. Volume 74. Springer, New York, NY, USA; 1989.

    Book  Google Scholar 

  5. Rabinowitz PH: Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conference Series in Mathematics. Volume 65. American Mathematical Society, Providence, RI, USA; 1986.

    Google Scholar 

  6. Ahlbrandt CD, Peterson AC: Discrete Hamiltonian Systems, Kluwer Texts in the Mathematical Sciences. Volume 16. Kluwer Academic Publishers, Dordrecht, The Netherlands; 1996.

    Book  Google Scholar 

  7. Bohner M: Linear Hamiltonian difference systems: disconjugacy and Jacobi-type conditions. Journal of Mathematical Analysis and Applications 1996,199(3):804–826. 10.1006/jmaa.1996.0177

    Article  MATH  MathSciNet  Google Scholar 

  8. Erbe LH, Yan PX: Disconjugacy for linear Hamiltonian difference systems. Journal of Mathematical Analysis and Applications 1992,167(2):355–367. 10.1016/0022-247X(92)90212-V

    Article  MATH  MathSciNet  Google Scholar 

  9. Hartman P: Difference equations: disconjugacy, principal solutions, Green's functions, complete monotonicity. Transactions of the American Mathematical Society 1978, 246: 1–30.

    MATH  MathSciNet  Google Scholar 

  10. Guo Z, Yu J: Periodic and subharmonic solutions for superquadratic discrete Hamiltonian systems. Nonlinear Analysis: Theory, Methods & Applications 2003,55(7–8):969–983. 10.1016/j.na.2003.07.019

    Article  MATH  MathSciNet  Google Scholar 

  11. Zhou Z, Yu J, Guo Z: The existence of periodic and subharmonic solutions to subquadratic discrete Hamiltonian systems. The ANZIAM Journal 2005,47(1):89–102. 10.1017/S1446181100009792

    Article  MATH  MathSciNet  Google Scholar 

  12. Guo Z, Yu J: Multiplicity results for periodic solutions to second-order difference equations. Journal of Dynamics and Differential Equations 2006,18(4):943–960. 10.1007/s10884-006-9042-1

    Article  MATH  MathSciNet  Google Scholar 

  13. Guo Z, Yu J: Existence of periodic and subharmonic solutions for second-order superlinear difference equations. Science in China A 2003,46(4):506–515.

    Article  MATH  MathSciNet  Google Scholar 

  14. Guo Z, Yu J: The existence of periodic and subharmonic solutions of subquadratic second order difference equations. Journal of the London Mathematical Society 2003,68(2):419–430. 10.1112/S0024610703004563

    Article  MATH  MathSciNet  Google Scholar 

  15. Zhou Z, Yu J, Guo Z: Periodic solutions of higher-dimensional discrete systems. Proceedings of the Royal Society of Edinburgh 2004,134(5):1013–1022. 10.1017/S0308210500003607

    Article  MATH  MathSciNet  Google Scholar 

  16. Chang K-C, Lin YQ: Functional Analysis(I). Peking University Press, Peking, China; 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China

    Bo Zheng

Authors
  1. Bo Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bo Zheng.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Zheng, B. Multiple Periodic Solutions to Nonlinear Discrete Hamiltonian Systems. Adv Differ Equ 2007, 041830 (2007). https://doi.org/10.1155/2007/41830

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/2007/41830

Keywords