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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 720139, 21 pages
http://dx.doi.org/10.1155/2012/720139
Research Article

Homoclinic Orbits for a Class of Noncoercive Discrete Hamiltonian Systems

1School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
2Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institute, Guangzhou University, Guangzhou 510006, China

Received 9 June 2012; Accepted 8 August 2012

Academic Editor: Wan-Tong Li

Copyright © 2012 Long Yuhua. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Poincar, Les Mthodes Nouvelles De La Mcanique Cleste, Gauthier-Villars, Paris, France, 1899.
  2. Y. Ding and M. Girardi, “Infinitely many homoclinic orbits of a Hamiltonian system with symmetry,” Nonlinear Analysis A, vol. 38, no. 3, pp. 391–415, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. H. Hofer and K. Wysocki, “First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems,” Mathematische Annalen, vol. 288, no. 3, pp. 483–503, 1990. View at Publisher · View at Google Scholar
  4. M. Ma and Z. Guo, “Homoclinic orbits for second order self-adjoint difference equations,” Journal of Mathematical Analysis and Applications, vol. 323, no. 1, pp. 513–521, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. J. Moser, Stable and Random Motions in Dynamical Systems, Princeton University Press, Princeton, NJ, USA, 1973.
  6. W. Omana and M. Willem, “Homoclinic orbits for a class of Hamiltonian systems,” Differential and Integral Equations, vol. 5, no. 5, pp. 1115–1120, 1992. View at Google Scholar · View at Zentralblatt MATH
  7. A. Szulkin and W. Zou, “Homoclinic orbits for asymptotically linear Hamiltonian systems,” Journal of Functional Analysis, vol. 187, no. 1, pp. 25–41, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. R. P. Agarwal, Difference Equations and Inequalities: Theory, Methods and Applications, Marcel Dekker, New York, NY, USA, 1992.
  9. S. N. Elaydi, An Introduction to Difference Equations, Springer, New York, NY, USA, 1996.
  10. W. G. Kelley and A. C. Peterson, Difference Equations: An Introduction with Applications, Academic Press, New York, NY, USA, 1991.
  11. V. L. Kocić and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic, Dodrecht, The Netherlands, 1993.
  12. R. E. Mickens, Difference Equations: Theory and Application, Van Nostrand Reinhold, New York, NY, USA, 1990.
  13. A. N. Sharkovsky, Y. L. Maĭstrenko, and E. Y. Romanenko, Difference Equations and Their Applications, Kluwer Academic, Dodrecht, The Netherlands, 1993. View at Publisher · View at Google Scholar
  14. Y. H. Long, “Multiplicity results for periodic solutions with prescribed minimal periods to discrete Hamiltonian systems,” Journal of Difference Equations and Applications, pp. 1–20, 2010. View at Google Scholar
  15. Z. Guo and J. Yu, “The existence of periodic and subharmonic solutions of subquadratic second order difference equations,” Journal of the London Mathematical Society, vol. 68, no. 2, pp. 419–430, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. Z. Zhou, J. Yu, and Z. Guo, “The existence of periodic and subharmonic solutions to subquadratic discrete Hamiltonian systems,” The ANZIAM Journal, vol. 47, no. 1, pp. 89–102, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. J. S. Yu, H. P. Shi, and Z. M. Guo, “Homoclinic orbits for nonlinear difference equations containing both advance and retardation,” Journal of Mathematical Analysis and Applications, vol. 352, no. 2, pp. 799–806, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. X. Deng and G. Cheng, “Homoclinic orbits for second order discrete Hamiltonian systems with potential changing sign,” Acta Applicandae Mathematicae, vol. 103, no. 3, pp. 301–314, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. Y. H. Long, “Homoclinic solutions of some second-order nonperiodic discrete systems,” Advances in Difference Equations, vol. 64, 12 pages, 2011. View at Publisher · View at Google Scholar
  20. P. Rabinowitz, “Minimax methods in critical point theory with applications to differential equations,” in Conference Board of the Mathematical Sciences (CBMS '89), vol. 65 of Regional Conference Series in Mathematics, 1986.