Open Access

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

Boundary Value Problems20072007:073176

DOI: 10.1155/2007/73176

Received: 12 October 2006

Accepted: 21 May 2007

Published: 4 July 2007

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.

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Authors’ Affiliations

(1)
Department of Mathematics, Yunnan University

References

  1. Bohner M, Peterson A: Dynamic Equations on Time Scales. An Introduction with Applications. Birkhäuser, Boston, Mass, USA; 2001:x+358.MATHView Article
  2. Bohner M, Peterson A (Eds): Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston, Mass, USA; 2003:xii+348.MATH
  3. Hilger S: Analysis on measure chains—a unified approach to continuous and discrete calculus. Results in Mathematics 1990,18(1–2):18–56.MATHMathSciNetView Article
  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. 10.1080/1026190290017405MATHMathSciNetView Article
  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. 10.1080/10236190410001667986MATHMathSciNetView Article
  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.2005.119MATHMathSciNetView Article
  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.MATHMathSciNet
  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.MATHMathSciNet
  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. 10.1080/00036819208840124MATHMathSciNetView Article
  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.View Article
  11. Kelley WG, Peterson AC: Difference Equations. An Introduction with Applications. Academic Press, Boston, Mass, USA; 1991:xii+455.MATH
  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.MATHMathSciNet

Copyright

© Y. Li and H. Zhang 2007

This article is published under license to BioMed Central Ltd. 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.