Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 374565, 11 pages
http://dx.doi.org/10.1155/2014/374565
Research Article

Boundary Value Problems for First-Order Impulsive Functional -Integrodifference Equations

1Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
2Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Received 11 November 2013; Revised 21 January 2014; Accepted 22 January 2014; Published 20 March 2014

Academic Editor: Allan Peterson

Copyright © 2014 Jessada Tariboon and Sotiris K. Ntouyas. 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. J. Tariboon and S. K. Ntouyas, “Quantum calculus on finite intervals and applications to impulsive difference equations,” Advances in Difference Equations, vol. 2013, article 282, 2013. View at Publisher · View at Google Scholar
  2. V. Kac and P. Cheung, Quantum Calculus, Springer, New York, NY, USA, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  3. G. Bangerezako, “Variational q-calculus,” Journal of Mathematical Analysis and Applications, vol. 289, no. 2, pp. 650–665, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  4. A. Dobrogowska and A. Odzijewicz, “Second order q-difference equations solvable by factorization method,” Journal of Computational and Applied Mathematics, vol. 193, no. 1, pp. 319–346, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  5. G. Gasper and M. Rahman, “Some systems of multivariable orthogonal q-Racah polynomials,” The Ramanujan Journal, vol. 13, no. 1–3, pp. 389–405, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  6. M. E. H. Ismail and P. Simeonov, “q-difference operators for orthogonal polynomials,” Journal of Computational and Applied Mathematics, vol. 233, no. 3, pp. 749–761, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. Bohner and G. Sh. Guseinov, “The h-Laplace and q-Laplace transforms,” Journal of Mathematical Analysis and Applications, vol. 365, no. 1, pp. 75–92, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  8. M. El-Shahed and H. A. Hassan, “Positive solutions of q-difference equation,” Proceedings of the American Mathematical Society, vol. 138, no. 5, pp. 1733–1738, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  9. B. Ahmad, “Boundary-value problems for nonlinear third-order q-difference equations,” Electronic Journal of Differential Equations, vol. 94, pp. 1–7, 2011. View at Google Scholar · View at MathSciNet
  10. B. Ahmad, A. Alsaedi, and S. K. Ntouyas, “A study of second-order q-difference equations with boundary conditions,” Advances in Difference Equations, vol. 2012, article 35, 2012. View at Publisher · View at Google Scholar
  11. B. Ahmad, S. K. Ntouyas, and I. K. Purnaras, “Existence results for nonlinear q-difference equations with nonlocal boundary conditions,” Communications on Applied Nonlinear Analysis, vol. 19, no. 3, pp. 59–72, 2012. View at Google Scholar · View at MathSciNet
  12. B. Ahmad and J. J. Nieto, “On nonlocal boundary value problems of nonlinear q-difference equations,” Advances in Difference Equations, vol. 2012, article 81, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  13. B. Ahmad and S. K. Ntouyas, “Boundary value problems for q-difference inclusions,” Abstract and Applied Analysis, vol. 2011, Article ID 292860, 15 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  14. W.-X. Zhou and H.-Z. Liu, “Existence solutions for boundary value problem of nonlinear fractional q-difference equations,” Advances in Difference Equations, vol. 2013, article 113, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  15. C. Yu and J. Wang, “Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives,” Advances in Difference Equations, vol. 2013, article 124, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  16. V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6, World Scientific Publishing, Singapore, 1989. View at MathSciNet
  17. A. M. Samoĭlenko and N. A. Perestyuk, Impulsive Differential Equations, vol. 14, World Scientific Publishing, Singapore, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  18. M. Benchohra, J. Henderson, and S. Ntouyas, Impulsive Differential Equations and Inclusions, vol. 2, Hindawi Publishing Corporation, New York, NY, USA, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  19. M. A. Krasnoselskii, “Two remarks on the method of successive approximations,” Uspekhi Matematicheskikh Nauk, vol. 10, pp. 123–127, 1955. View at Google Scholar · View at MathSciNet