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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 417020, 7 pages
http://dx.doi.org/10.1155/2013/417020
Research Article

Homoclinic Solutions for a Second-Order Nonperiodic Asymptotically Linear Hamiltonian Systems

College of Computer Science and Technology, Shandong University of Technology, Zibo, Shandong 255049, China

Received 18 November 2012; Accepted 21 December 2012

Academic Editor: Juntao Sun

Copyright © 2013 Qiang Zheng. 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. J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, vol. 74, Springer, New York, NY, USA, 1989. View at MathSciNet
  2. P. H. Rabinowitz, “Variational methods for Hamiltonian systems,” in Handbook of Dynamical Systems, vol. 1, part 1, chapter 14, pp. 1091–1127, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. Daouas, “Homoclinic orbits for superquadratic Hamiltonian systems without a periodicity assumption,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 11, pp. 3407–3418, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Y. Ding, “Multiple homoclinics in a Hamiltonian system with asymptotically or super linear terms,” Communications in Contemporary Mathematics, vol. 8, no. 4, pp. 453–480, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. Y. Ding and C. Lee, “Existence and exponential decay of homoclinics in a nonperiodic superquadratic Hamiltonian system,” Journal of Differential Equations, vol. 246, no. 7, pp. 2829–2848, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. Y. Ding and L. Jeanjean, “Homoclinic orbits for a nonperiodic Hamiltonian system,” Journal of Differential Equations, vol. 237, no. 2, pp. 473–490, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. Sun, H. Chen, and J. J. Nieto, “Homoclinic orbits for a class of first-order nonperiodic asymptotically quadratic Hamiltonian systems with spectrum point zero,” Journal of Mathematical Analysis and Applications, vol. 378, no. 1, pp. 117–127, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Y. H. Ding, “Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 25, no. 11, pp. 1095–1113, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. Izydorek and J. Janczewska, “Homoclinic solutions for a class of the second order Hamiltonian systems,” Journal of Differential Equations, vol. 219, no. 2, pp. 375–389, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. Izydorek and J. Janczewska, “Homoclinic solutions for nonautonomous second order Hamiltonian systems with a coercive potential,” Journal of Mathematical Analysis and Applications, vol. 335, no. 2, pp. 1119–1127, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. X. Lv, S. Lu, and P. Yan, “Homoclinic solutions for nonautonomous second-order Hamiltonian systems with a coercive potential,” Nonlinear Analysis: Theory, Methods & Applications, vol. 72, no. 7-8, pp. 3484–3490, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. P. H. Rabinowitz, “Homoclinic orbits for a class of Hamiltonian systems,” Proceedings of the Royal Society of Edinburgh A, vol. 114, no. 1-2, pp. 33–38, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. P. H. Rabinowitz and K. Tanaka, “Some results on connecting orbits for a class of Hamiltonian systems,” Mathematische Zeitschrift, vol. 206, no. 3, pp. 473–499, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J. Sun, H. Chen, and J. J. Nieto, “Homoclinic solutions for a class of subquadratic second-order Hamiltonian systems,” Journal of Mathematical Analysis and Applications, vol. 373, no. 1, pp. 20–29, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. X. H. Tang and X. Lin, “Homoclinic solutions for a class of second-order Hamiltonian systems,” Journal of Mathematical Analysis and Applications, vol. 354, no. 2, pp. 539–549, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. X. H. Tang and L. Xiao, “Homoclinic solutions for a class of second-order Hamiltonian systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 3-4, pp. 1140–1152, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. L.-L. Wan and C.-L. Tang, “Existence and multiplicity of homoclinic orbits for second order Hamiltonian systems without (AR) condition,” Discrete and Continuous Dynamical Systems B, vol. 15, no. 1, pp. 255–271, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. Z. Zhang and R. Yuan, “Homoclinic solutions for a class of non-autonomous subquadratic second-order Hamiltonian systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 9, pp. 4125–4130, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. Z. Zhang and R. Yuan, “Homoclinic solutions for some second order non-autonomous Hamiltonian systems with the globally superquadratic condition,” Nonlinear Analysis: Theory, Methods & Applications, vol. 72, no. 3-4, pp. 1809–1819, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  20. P. Korman and A. C. Lazer, “Homoclinic orbits for a class of symmetric Hamiltonian systems,” Electronic Journal of Differential Equations, vol. 1994, pp. 1–10, 1994. View at Zentralblatt MATH · View at MathSciNet
  21. P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, vol. 65 of CBMS, 1986.
  22. P. Bartolo, V. Benci, and D. Fortunato, “Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity,” Nonlinear Analysis: Theory, Methods & Applications, vol. 7, no. 9, pp. 981–1012, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet