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Abstract and Applied Analysis
Volume 2014, Article ID 960276, 12 pages
http://dx.doi.org/10.1155/2014/960276
Research Article

Existence and Multiplicity of Fast Homoclinic Solutions for a Class of Damped Vibration Problems with Impulsive Effects

College of Science, Guilin University of Technology, Guilin, Guangxi 541004, China

Received 11 April 2014; Accepted 26 May 2014; Published 15 June 2014

Academic Editor: Jianqing Chen

Copyright © 2014 Qiongfen Zhang. 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. P. Chen, X. Tang, and R. P. Agarwal, “Fast homoclinic solutions for a class of damped vibration problems,” Applied Mathematics and Computation, vol. 219, no. 11, pp. 6053–6065, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. H. Fang and H. Duan, “Existence of nontrivial weak homoclinic orbits for second-order impulsive differential equations,” Boundary Value Problems, vol. 2012, article 138, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. D. D. Bainov and P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman Scientific & Tecgnical, New York, NY, USA, 1993.
  4. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific Press, Singapore, 1989.
  5. P. Chen and X. H. Tang, “New existence and multiplicity of solutions for some Dirichlet problems with impulsive effects,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 723–739, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. H. Chen and J. Sun, “An application of variational method to second-order impulsive differential equation on the half-line,” Applied Mathematics and Computation, vol. 217, no. 5, pp. 1863–1869, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. Q. Zhang, W.-Z. Gong, and X. H. Tang, “Existence of subharmonic solutions for a class of second-order p-Laplacian systems with impulsive effects,” Journal of Applied Mathematics, vol. 2012, Article ID 434938, 18 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. Z. Luo, J. Xiao, and Y. Xu, “Subharmonic solutions with prescribed minimal period for some second-order impulsive differential equations,” Nonlinear Analysis: Theory, Methods and Applications, vol. 75, no. 4, pp. 2249–2255, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. J. J. Nieto and D. O'Regan, “Variational approach to impulsive differential equations,” Nonlinear Analysis: Real World Applications, vol. 10, no. 2, pp. 680–690, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. J. Sun and H. Chen, “Variational method to the impulsive equation with neumann boundary conditions,” Boundary Value Problems, vol. 2009, Article ID 316812, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. J. Sun, H. Chen, and L. Yang, “The existence and multiplicity of solutions for an impulsive differential equation with two parameters via a variational method,” Nonlinear Analysis: Theory, Methods and Applications, vol. 73, no. 2, pp. 440–449, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  12. J. Sun, H. Chen, J. J. Nieto, and M. Otero-Novoa, “The multiplicity of solutions for perturbed second-order Hamiltonian systems with impulsive effects,” Nonlinear Analysis: Theory, Methods and Applications, vol. 72, no. 12, pp. 4575–4586, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. J. Sun, H. Chen, and J. J. Nieto, “Infinitely many solutions for second-order Hamiltonian system with impulsive effects,” Mathematical and Computer Modelling, vol. 54, no. 1-2, pp. 544–555, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. D. Zhang and B. Dai, “Existence of solutions for nonlinear impulsive differential equations with Dirichlet boundary conditions,” Mathematical and Computer Modelling, vol. 53, no. 5-6, pp. 1154–1161, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. Z. Zhang and R. Yuan, “An application of variational methods to Dirichlet boundary value problem with impulses,” Nonlinear Analysis: Real World Applications, vol. 11, no. 1, pp. 155–162, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  16. J. Zhou and Y. Li, “Existence and multiplicity of solutions for some Dirichlet problems with impulsive effects,” Nonlinear Analysis: Theory, Methods and Applications, vol. 71, no. 7-8, pp. 2856–2865, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  17. J. Zhou and Y. Li, “Existence of solutions for a class of second-order Hamiltonian systems with impulsive effects,” Nonlinear Analysis: Theory, Methods and Applications, vol. 72, no. 3-4, pp. 1594–1603, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  18. X. Han and H. Zhang, “Periodic and homoclinic solutions generated by impulses for asymptotically linear and sublinear Hamiltonian system,” Journal of Computational and Applied Mathematics, vol. 235, no. 5, pp. 1531–1541, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  19. H. Zhang and Z. Li, “Periodic and homoclinic solutions generated by impulses,” Nonlinear Analysis: Real World Applications, vol. 12, no. 1, pp. 39–51, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  20. 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 Scopus
  21. P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, vol. 65 of CBMS Regional Conference Series in Mathematics, The American Mathematical Society, Providence, RI, USA, 1986.
  22. X. H. Tang and X. Lin, “Existence of infinitely many homoclinic orbits in Hamiltonian systems,” Proceedings of the Royal Society of Edinburgh A: Mathematics, vol. 141, no. 5, pp. 1103–1119, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus