Skip to main content
Boundary Value Problems
Download PDF

Extremal Solutions of Periodic Boundary Value Problems for First-Order Impulsive Integrodifferential Equations of Mixed-Type on Time Scales

Boundary Value Problems volume 2007, Article number: 073176 (2007) Cite this article

Abstract

We consider the existence of minimal and maximal solutions of periodic boundary value problems for first-order impulsive integrodifferential equations of mixed-type on time scales by establishing a comparison result and using the monotone iterative technique.

[123456789101112]

References

  1. 1.

    Bohner M, Peterson A: Dynamic Equations on Time Scales. An Introduction with Applications. Birkhäuser, Boston, Mass, USA; 2001:x+358.

    MATH  Book  Google Scholar 

  2. 2.

    Bohner M, Peterson A (Eds): Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston, Mass, USA; 2003:xii+348.

    MATH  Google Scholar 

  3. 3.

    Hilger S: Analysis on measure chains—a unified approach to continuous and discrete calculus. Results in Mathematics 1990,18(1–2):18–56.

    MATH  MathSciNet  Article  Google Scholar 

  4. 4.

    Henderson J: Double solutions of impulsive dynamic boundary value problems on a time scale. Journal of Difference Equations and Applications 2002,8(4):345–356. 10.1080/1026190290017405

    MATH  MathSciNet  Article  Google Scholar 

  5. 5.

    Benchohra M, Henderson J, Ntouyas SK, Ouahab A: On first order impulsive dynamic equations on time scales. Journal of Difference Equations and Applications 2004,10(6):541–548. 10.1080/10236190410001667986

    MATH  MathSciNet  Article  Google Scholar 

  6. 6.

    Atici FM, Biles DC: First- and second-order dynamic equations with impulse. Advances in Difference Equations 2005,2005(2):119–132. 10.1155/ADE.2005.119

    MATH  MathSciNet  Article  Google Scholar 

  7. 7.

    Liu X, Guo D: Periodic boundary value problems for impulsive integro-differential equations of mixed type in Banach spaces. Chinese Annals of Mathematics. Series B 1998,19(4):517–528.

    MATH  MathSciNet  Google Scholar 

  8. 8.

    Ladde GS, Sathananthan S: Periodic boundary value problem for impulsive integro-differential equations of Volterra type. Journal of Mathematical and Physical Sciences 1991,25(2):119–129.

    MATH  MathSciNet  Google Scholar 

  9. 9.

    Erbe LH, Guo DJ: Periodic boundary value problems for second order integrodifferential equations of mixed type. Applicable Analysis 1992,46(3–4):249–258. 10.1080/00036819208840124

    MATH  MathSciNet  Article  Google Scholar 

  10. 10.

    Lakshmikantham V, Baĭnov DD, Simeonov PS: Theory of Impulsive Differential Equations, Series in Modern Applied Mathematics. Volume 6. World Scientific, Teaneck, NJ, USA; 1989:xii+273.

    Book  Google Scholar 

  11. 11.

    Kelley WG, Peterson AC: Difference Equations. An Introduction with Applications. Academic Press, Boston, Mass, USA; 1991:xii+455.

    MATH  Google Scholar 

  12. 12.

    Xing Y, Han M, Zheng G: Initial value problem for first-order integro-differential equation of Volterra type on time scales. Nonlinear Analysis: Theory, Methods & Applications 2005,60(3):429–442.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Affiliations

  1. Department of Mathematics, Yunnan University, Kunming, Yunnan, 650091, China

    Yongkun Li & Hongtao Zhang

Authors
  1. Yongkun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hongtao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yongkun Li.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Li, Y., Zhang, H. Extremal Solutions of Periodic Boundary Value Problems for First-Order Impulsive Integrodifferential Equations of Mixed-Type on Time Scales. Bound Value Probl 2007, 073176 (2007). https://doi.org/10.1155/2007/73176

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/2007/73176

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Comparison Result