Table of Contents Author Guidelines Submit a Manuscript
Journal of Mathematics
Volume 2014 (2014), Article ID 214093, 13 pages
http://dx.doi.org/10.1155/2014/214093
Research Article

Multiple Positive Periodic Solutions for Two Kinds of Higher-Dimension Impulsive Differential Equations with Multiple Delays and Two Parameters

1Department of Mathematics, Hengyang Normal University, Hengyang, Hunan 421008, China
2Department of Mathematics, National University of Defense Technology, Changsha 410073, China

Received 8 September 2013; Revised 13 February 2014; Accepted 13 February 2014; Published 6 April 2014

Academic Editor: Nan-Jing Huang

Copyright © 2014 Zhenguo Luo. 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. V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989. View at MathSciNet
  2. D. D. Bainov and P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman Scientific and Technical, London, UK, 1993.
  3. A. M. Samoikleno and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995. View at MathSciNet
  4. S. T. Zavalishchin and A. N. Sesekin, Dynamic Impulse Systems, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997. View at MathSciNet
  5. D. Q. Jiang and J. J. Wei, “Existence of positive periodic solutions for nonautonomous delay differential equations,” Chinese Annals of Mathematics A, vol. 20, no. 6, pp. 715–720, 1999 (Chinese). View at Google Scholar · View at MathSciNet
  6. A. M. Zhao, W. P. Yan, and J. R. Yan, “Existence of positive periodic solution for an impulsive delay differential equation,” in Topological Methods, Variational Methods and Their Applications, pp. 269–274, World Scientific, London, UK, 2002. View at Google Scholar
  7. H.-F. Huo, W.-T. Li, and X. Liu, “Existence and global attractivity of positive periodic solution of an impulsive delay differential equation,” Applicable Analysis, vol. 83, no. 12, pp. 1279–1290, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  8. X. Y. Zhang, J. R. Yan, and A. P. Zhao, “Existence of positive periodic solutions for an impulsive differential equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 10, pp. 3209–3216, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. R. Yan, “Existence of positive periodic solutions of impulsive functional differential equations with two parameters,” Journal of Mathematical Analysis and Applications, vol. 327, no. 2, pp. 854–868, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. Z. J. Zeng, L. Bi, and M. Fan, “Existence of multiple positive periodic solutions for functional differential equations,” Journal of Mathematical Analysis and Applications, vol. 325, no. 2, pp. 1378–1389, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. R. Yan, “Global attractivity for impulsive population dynamics with delay arguments,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 11, pp. 5417–5426, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. G. Ballinger and X. Z. Liu, “Existence, uniqueness and boundedness results for impulsive delay differential equations,” Applicable Analysis, vol. 74, no. 1-2, pp. 71–93, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. D. Lin, X. D. Li, and D. O'Regan, “Stability analysis of generalized impulsive functional differential equations,” Mathematical and Computer Modelling, vol. 55, no. 5-6, pp. 1682–1690, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Z. G. Luo, L. P. Luo, and Y. H. Zeng, “Positive periodic solutions for impulsive functional differential equations with infinite delay and two parameters,” Journal of Applied Mathematics, vol. 2014, Article ID 751612, 17 pages, 2014. View at Publisher · View at Google Scholar
  15. X. D. Li and X. L. Fu, “On the global exponential stability of impulsive functional differential equations with infinite delays or finite delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 3, pp. 442–447, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  16. Z. G. Luo, B. X. Dai, and Q. H. Zhang, “Existence of positive periodic solutions for an impulsive semi-ratio-dependent predator-prey model with dispersion and time delays,” Applied Mathematics and Computation, vol. 215, no. 9, pp. 3390–3398, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. X. Q. Ding, C. W. Wang, and P. Chen, “Permanence for a two-species Gause-type ratio-dependent predator-prey system with time delay in a two-patch environment,” Applied Mathematics and Computation, vol. 219, no. 17, pp. 9099–9105, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  18. J. R. Yan and A. M. Zhao, “Oscillation and stability of linear impulsive delay differential equations,” Journal of Mathematical Analysis and Applications, vol. 227, no. 1, pp. 187–194, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. D. J. Guo, Nonlinear Functional Analysis, ShanDong Science and Technology Press, Ji'nan, China, 2001.
  20. M. A. Krasnoselskii, Positive Solution of Operator Equation, P. Noordhoff, Groningen, The Netherlands, 1964.
  21. K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985. View at MathSciNet
  22. D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, Orlando, Fla, USA, 1988. View at MathSciNet