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International Journal of Differential Equations
Volume 2014 (2014), Article ID 791240, 12 pages
http://dx.doi.org/10.1155/2014/791240
Research Article

Periodic Boundary Value Problems for First-Order Impulsive Functional Integrodifferential Equations with Integral-Jump Conditions

1Department of Mathematics, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Bangkok 10520, Thailand
2Centre of Excellence in Mathematics, CHE, Sri Ayutthaya Road, Bangkok 10400, Thailand
3Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand

Received 6 January 2014; Accepted 11 February 2014; Published 23 March 2014

Academic Editor: Kanishka Perera

Copyright © 2014 Chatthai Thaiprayoon et al. 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.

Linked References

  1. D. D. Bainov and P. S. Simeonov, Impulsive Differential Equations: Asymptotic Properties of the Solutions, vol. 28 of Series on Advances in Mathematics for Applied Sciences, World Scientific, Singapore, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  2. D. D. Bainov and P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman Scientific and Technical, Harlow, UK, 1993.
  3. M. Benchohra, J. Henderson, and S. Ntouyas, Impulsive Differential Equations and Inclusions, vol. 2 of Contemporary Mathematics and Its Applications, Hindawi Publishing Corporation, New York, NY, USA, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  4. V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific, Singapore, 1989. View at MathSciNet
  5. A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  6. G. S. Ladde, V. Lakshmikantham, and A. S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations, Advanced Texts and Surveys in Pure and Applied Mathematics, Pitman, Boston, Mass, USA, 1985. View at MathSciNet
  7. B. Ahmad and J. J. Nieto, “Existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti-periodic boundary conditions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 10, pp. 3291–3298, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. L. Chen and J. Sun, “Nonlinear boundary value problem for first order impulsive integro-differential equations of mixed type,” Journal of Mathematical Analysis and Applications, vol. 325, no. 2, pp. 830–842, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. X. He, J. Xie, G. Chen, and J. Shen, “Integral BVPs for a class of first-order impulsive functional differential equations,” International Journal of Differential Equations, vol. 2010, Article ID 908960, 11 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. T. Jankowski, “First-order impulsive ordinary differential equations with advanced arguments,” Journal of Mathematical Analysis and Applications, vol. 331, no. 1, pp. 1–12, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Li and J. Shen, “New comparison results for impulsive functional differential equations,” Applied Mathematics Letters, vol. 23, no. 4, pp. 487–493, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Z. Luo and J. J. Nieto, “New results for the periodic boundary value problem for impulsive integro-differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 6, pp. 2248–2260, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. G. Wang, L. Zhang, and G. Song, “New existence results and comparison principles for impulsive integral boundary value problem with lower and upper solutions in reversed order,” Advances in Difference Equations, vol. 2011, Article ID 783726, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. X. Yang and J. Shen, “Nonlinear boundary value problems for first order impulsive functional differential equations,” Applied Mathematics and Computation, vol. 189, no. 2, pp. 1943–1952, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. L. Zhang, “Boundary value problem for first order impulsive functional integro-differential equations,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2442–2450, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. Z. Liu, J. Han, and L. Fang, “Integral boundary value problems for first order integro-differential equations with impulsive integral conditions,” Computers & Mathematics with Applications, vol. 61, no. 10, pp. 3035–3043, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. Z. Liu, J. Han, and L. Fang, “Nonlinear boundary value problems for first order integro-differential equations with impulsive integral conditions,” Bulletin of the Malaysian Mathematical Sciences Society, vol. 36, no. 2, pp. 435–446, 2013. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. J. Tariboon, “Boundary value problems for first order functional differential equations with impulsive integral conditions,” Journal of Computational and Applied Mathematics, vol. 234, no. 8, pp. 2411–2419, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. C. Thaiprayoon, D. Samana, and J. Tariboon, “Multi-point boundary value problem for first order impulsive integro-differential equations with multi-point jump conditions,” Boundary Value Problems, vol. 2012, article 38, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. P. Thiramanus and J. Tariboon, “Impulsive differential and impulsive integral inequalities with integral jump conditions,” Journal of Inequalities and Applications, vol. 2012, article 25, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. D. R. Smart, Fixed Point Theorems, Cambridge University Press, Cambridge, UK, 1980. View at MathSciNet