Skip to main content
SpringerLink
Log in

Positive periodic solutions of functional differential equations with impulse on time scales

  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

In this paper, we employ some analysis technics to study the existence of positive periodic solutions to a system of equations with a parameter and impulse on time scales.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Zhang, G., Cheng, S.S.: Positive periodic solution of nonautonomous function differential equations depending on a parameter. Appl. Anal. 7(5), 279–286 (2002)

    MATH  MathSciNet  Google Scholar 

  2. Chow, S.-N.: Existence of periodic solution of autonomous functional differential equations. J. Math. Anal. Appl. 15, 350–387 (1974)

    MATH  Google Scholar 

  3. Zhu, L., Li, Y.: Positive periodic solutions of higher-dimensional functional difference equations with a parameter. J. Math. Anal. Appl. 290, 654–664 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Kang, S., Zhang, G., Shi, B.: Existence of three periodic positive solutions for a class of integral equations with parameters. J. Math. Anal. Appl. 323, 654–665 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  5. Zeng, Z., Bi, L., Fan, M.: Existence of multiple positive periodic solutions for functional differential equations. J. Math. Anal. Appl. 325, 1378–1389 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Li, Y., Zhu, L., Liu, P.: Positive periodic solutions of nonlinear functional difference equations depending on a parameter. Comput. Math. Appl. 48, 1453–1459 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hadeler, L., Krisztin, T.: On the existence of periodic solution for linear inhomogeneous and quasilinear functional differential equations. J. Differ. Equ. 97, 1–15 (1992)

    Article  Google Scholar 

  8. Liu, P., Li, Y.: Positive periodic solutions of infinite delay functional equations depending on a parameter. Appl. Math. Comput. 150, 159–168 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  9. Makay, G.: Periodic solutions of dissipative functional differential equations. Tôhoku Math. J. 46, 417–426 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  10. Li, Y.: Existence and global attractivity of a positive periodic solution of a class of delay differential equation. Sci. China Ser. A 41, 273–284 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  11. Li, Y., Kuang, Y.: Periodic solution of periodic Lotka-Volterra equation and systems. J. Math. Anal. Appl. 255, 260–280 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Li, Y.: Positive periodic solutions of nonlinear differential systems with impulses. Nonlinear Anal. 8, 2389–2405 (2008)

    Google Scholar 

  13. Kuang, Y.: Delay Differential Equations with Applications in Population Dynamics. Academic Press, New York (1993)

    MATH  Google Scholar 

  14. Zhen, J., Ma, Z., Han, M.: The existence of periodic solutions of the n-species Lotka-Volterra competition systems with impulsive. Chaos Solutions Fractals 22(1), 181–188 (2004)

    Article  MATH  Google Scholar 

  15. Li, Y.K.: Periodic solutions for delay Lotka-Volterra competition systems. J. Math. Appl. Anal. 246, 230–244 (2000)

    Article  MATH  Google Scholar 

  16. Sun, W., Chen, S.H., Hong, Z.M., Wang, C.G.: On positive periodic solution of periodic competitive Lotka-Volterra system with time delay and diffusion. Chaos Solutions Fractals 33, 971–978 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  17. Liao, X.Y., Ouyang, Z.G., Zhou, S.Q.: Permanence of species in nonautonomous discrete Lotka-Volterra competitive system with delays and feedback controls. J. Comput. Appl. Math. 211, 1–10 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  18. Li, J.X., Yan, J.R.: Partial permanence and extinction in an N-species nonautonomous Lotka-Volterra competitive system. Comput. Appl. Math. 55, 76–88 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  19. Wang, C.Z., Shi, J.L.: Positive almost periodic solutions of a class of Lotka-Volterra type competitive system with delays and feedback controls. Appl. Math. Comput. 193, 240–252 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  20. Bohner, M., Peterson, A.: Dynamic Equations on Time Scales, An Introduction with Applications. Birkhäuser, Boston (2001)

    MATH  Google Scholar 

  21. Kaufmann, E.R., Raffoul, Y.N.: Periodic solutions for a neutral nonlinear dynamical equation on time scale. J. Math. Appl. 319, 315–325 (2006)

    MATH  MathSciNet  Google Scholar 

  22. Xing, Y., Han, M., Zheng, G.: Initial value problem for first-order integro-differential equation of Volterra type on time scale. Nonlinear Anal. 60, 429–442 (2005)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Yunnan University, Kunming, Yunnan, 650091, People’s Republic of China

    Yongkun Li, Lu Zhao & Xuerong Chen

Authors
  1. Yongkun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lu Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xuerong Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yongkun Li.

Additional information

This work is supported by the National Natural Sciences Foundation of People’s Republic of China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, Y., Zhao, L. & Chen, X. Positive periodic solutions of functional differential equations with impulse on time scales. J. Appl. Math. Comput. 34, 495–510 (2010). https://doi.org/10.1007/s12190-009-0334-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-009-0334-6

Keywords

Mathematics Subject Classification (2000)

Search

Navigation