Skip to main content
Log in

Periodic boundary value problem for the first order functional differential equations with impulses

  • Published:
Applied Mathematics-A Journal of Chinese Universities Aims and scope Submit manuscript

Abstract

This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is presented and the previous results are extended.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Lakshmikantham V, Bainov D D, Simeonov P S. Theory of Impulsive Differential Equations, Singapore: World Scientific, 1989.

    MATH  Google Scholar 

  2. Bainov D D, Simeonov P S. Impulsive Differential Equations: Periodic Solutions and Applications, Harlow: Longman Scientific and Technical, 1993.

    MATH  Google Scholar 

  3. Samoilenko A M, Perestyuk N A. Impulsive Differential Equations, Singapore: World Scientific, 1995.

    MATH  Google Scholar 

  4. Rogovchenko Y V. Impulsive evolution systems: Main results and new trends, Dynamics of Continuous Discrete Impulsive Systems, 1997, 3: 57–88.

    MATH  MathSciNet  Google Scholar 

  5. He Z M, Yu J S. Periodic boundary value problem for first order impulsive functional differential equations, J Comput Appl Math, 2002, 138: 205–217.

    Article  MATH  MathSciNet  Google Scholar 

  6. Li J L, Shen J H. Periodic boundary value problems for impulsive differential difference equations, Indian J Pure Appl Math, 2004, 35(11): 1265–1277.

    MATH  MathSciNet  Google Scholar 

  7. Franco D, Liz E, Nieto J J, et al. A contribution to the study of functional differential equations with impulses, Math Nachr, 2000, 218: 49–60.

    Article  MATH  MathSciNet  Google Scholar 

  8. Nieto J J. Periodic boundary value problems for first order impulsive ordinary differential equations, Nonlinear Anal, 2002, 51: 1223–1232.

    Article  MATH  MathSciNet  Google Scholar 

  9. Chen L J, Sun J T. Boundary value problem of second order impulsive functional differential equations, J Math Anal Appl, 2006, 323: 708–720.

    Article  MATH  MathSciNet  Google Scholar 

  10. He X M, Ge W G, He Z M. First-order impulsive functional differential equations with periodic boundary value conditions, Indian J Pure Appl Math, 2002, 33: 1257–1273.

    MATH  MathSciNet  Google Scholar 

  11. Zhang F, Ma Z E, Yan J R. Periodic boundary value problems and monotone iterative methods for first-order impulsive differential equations with delay, Indian J Pure Appl Math, 2001, 32: 1695–1707.

    MATH  MathSciNet  Google Scholar 

  12. Dong Y. Periodic boundary value problems for functional -differential equations with impulses, J Math Anal Appl, 1997, 210: 170–181.

    Article  MATH  MathSciNet  Google Scholar 

  13. Nieto J J, Rodriguez-Lopez R. Periodic boundary value problem for non-Lipschitzian impulsive functional differential equations, J Math Anal Appl, 2006, 318: 593–610.

    Article  MATH  MathSciNet  Google Scholar 

  14. Ding W, Mi J R. Periodic boundary value problems for the first impulsive functional differential equation, Appl Math Comput, 2005, 165: 433–446.

    Article  MATH  MathSciNet  Google Scholar 

  15. Nieto J J. Basic theory for nonresonance impulsive periodic problems of first order, J Math Anal Appl, 1997, 205: 423–433.

    Article  MATH  MathSciNet  Google Scholar 

  16. He Z M, Ge W G. Periodic boundary value problem for first order impulsive delay differential equation, Appl Math Comput, 1999, 104: 51–63.

    Article  MATH  MathSciNet  Google Scholar 

  17. Ding W, Han M A. Periodic boundary value problem for second order impulsive functional differential equations, Appl Math Comput, 2004, 155: 709–726.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported by the National Natural Science Foundation of China (10571050; 10871062) and Hunan Provincial Innovation Foundation For Postgraduate

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liang, Rx., Shen, Jh. Periodic boundary value problem for the first order functional differential equations with impulses. Appl. Math. J. Chin. Univ. 24, 27–35 (2009). https://doi.org/10.1007/s11766-009-1921-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11766-009-1921-x

MR Subject Classification

Keywords

Navigation