SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Research Article

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

Yongkun Li* and Hongtao Zhang

Author Affiliations

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

For all author emails, please log on.

Boundary Value Problems 2007, 2007:073176  doi:10.1155/2007/73176

The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2007/1/073176


Received:12 October 2006
Accepted:21 May 2007
Published:4 July 2007

© 2007 Li and Zhang

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.

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.

References

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

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

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

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

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

  6. Atici, FM, Biles, DC: First- and second-order dynamic equations with impulse. Advances in Difference Equations. 2005(2), 119–132 (2005). Publisher Full Text OpenURL

  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. 19(4), 517–528 (1998)

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

  9. Erbe, LH, Guo, DJ: Periodic boundary value problems for second order integrodifferential equations of mixed type. Applicable Analysis. 46(3-4), 249–258 (1992). Publisher Full Text OpenURL

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

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

  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. 60(3), 429–442 (2005). PubMed Abstract | Publisher Full Text OpenURL