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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 140173, 9 pages
http://dx.doi.org/10.1155/2013/140173
Research Article

Nontrivial Periodic Solutions of an -Dimensional Differential System and Its Application

School of Mathematical Science, Yangzhou University, Yangzhou 225002, China

Received 29 March 2013; Accepted 3 August 2013

Academic Editor: Pei Yu

Copyright © 2013 F. B. Gao. 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. S. I. Chang, A. K. Bajaj, and C. M. Krousgrill, “Nonlinear vibrations and chaos in harmonically excited rectangular plates with one-to-one internal resonance,” Nonlinear Dynamics, vol. 4, pp. 433–460, 1993.
  2. A. F. Dizaji, H. A. Sepiani, F. E. Ebrahimi, A. Allahverdizadeh, and H. A. Sepiani, “Schauder fixed point theorem based existence of periodic solution for the response of Duffing's oscillator,” Journal of Mechanical Science and Technology, vol. 23, pp. 2299–2307, 2009.
  3. N. Malhotra and N. S. Namachchivaya, “Chaotic dynamics of shallow arch structures under 1 : 1 internal resonance conditions,” Journal of Engineering Mechanics, vol. 123, pp. 612–619, 1997.
  4. W. M. Tian, N. S. Namachchivaya, and N. Malhotra, “Nonlinear dynamics of a shallow arch under periodic excitation-II. 1 : 1 internal resonance,” International Journal of Non-Linear Mechanics, vol. 29, pp. 367–386, 1994.
  5. W. Zhang, “Global and chaotic dynamics for a parametrically excited thin plate,” Journal of Sound and Vibration, vol. 239, pp. 1013–1036, 2001.
  6. W. Zhang, F. B. Gao, and L. H. Chen, “Periodic solutions for a thin plate with parametrical excitation,” in Proceedings of the 12th NCNV and 9th NCNDSM, Zhenjiang, China, 2009.
  7. P. Amster, P. De Nápoli, and M. C. Mariani, “Periodic solutions for p-Laplacian like systems with delay,” Dynamics of Continuous, Discrete & Impulsive Systems, vol. 13, no. 3-4, pp. 311–319, 2006. View at MathSciNet
  8. W. S. Cheung and J. L. Ren, “Periodic solutions for p-Laplacian Rayleigh equations,” Nonlinear Analysis. Theory, Methods & Applications, vol. 65, no. 10, pp. 2003–2012, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  9. F. B. Gao, W. Zhang, S. K. Lai, and S. P. Chen, “Periodic solutions for n-generalized Liénard type p-Laplacian functional differential system,” Nonlinear Analysis. Theory, Methods & Applications, vol. 71, no. 12, pp. 5906–5914, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  10. F. B. Gao and W. Zhang, “Periodic solutions for a p-Laplacian-like NFDE system,” Journal of the Franklin Institute, vol. 348, no. 6, pp. 1020–1034, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  11. F. B. Gao, S. P. Lu, and W. Zhang, “Existence and uniqueness of periodic solutions for a p-Laplacian Duffing equation with a deviating argument,” Nonlinear Analysis. Theory, Methods & Applications, vol. 70, no. 10, pp. 3567–3574, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  12. R. Manásevich and J. Mawhin, “Periodic solutions for nonlinear systems with p-Laplacian-like operators,” Journal of Differential Equations, vol. 145, no. 2, pp. 367–393, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  13. M. L. Bertotti and M. Delitala, “On the existence of limit cycles in opinion formation processes under time periodic influence of persuaders,” Mathematical Models & Methods in Applied Sciences, vol. 18, no. 6, pp. 913–934, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  14. D. Jiang, D. O'Regan, R. P. Agarwal, and X. Xu, “On the number of positive periodic solutions of functional differential equations and population models,” Mathematical Models & Methods in Applied Sciences, vol. 15, no. 4, pp. 555–573, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  15. L. Nie, Z. Teng, and L. Hu, “Existence and stability of periodic solution of a stage-structured model with state-dependent impulsive effects,” Mathematical Methods in the Applied Sciences, vol. 34, no. 14, pp. 1685–1693, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  16. R. Ouifki and M. L. Hbid, “Periodic solutions for a class of functional differential equations with state-dependent delay close to zero,” Mathematical Models & Methods in Applied Sciences, vol. 13, no. 6, pp. 807–841, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  17. S. P. Lu and W. G. Ge, “Sufficient conditions for the existence of periodic solutions to some second order differential equations with a deviating argument,” Journal of Mathematical Analysis and Applications, vol. 308, no. 2, pp. 393–419, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  18. R. E. Gaines and J. L. Mawhin, Coincidence Degree, and Nonlinear Differential Equations, Springer, Berlin, Germany, 1977. View at MathSciNet
  19. C. Y. Chia, Nonlinear Analysis of Plate, McMraw-Hill, New York, NY, USA, 1980.