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Mathematical Problems in Engineering
Volume 2009, Article ID 258090, 16 pages
http://dx.doi.org/10.1155/2009/258090
Research Article

MultiPoint BVPs for Second-Order Functional Differential Equations with Impulses

1Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, China
2Department of Mathematics, Hunan First Normal University, Changsha, Hunan 410205, China
3College of Science, Zhejiang Forestry University, Hangzhou, Zhejiang 311300, China
4Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China

Received 14 April 2009; Accepted 10 June 2009

Academic Editor: Fernando Lobo Pereira

Copyright © 2009 Xuxin Yang 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. G. S. Ladde, V. Lakshmikantham, and A. S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations, vol. 27 of Monographs, Advanced Texts and Surveys in Pure and Applied Mathematics, Pitman Advanced Publishing Program, London, UK, 1985. View at MathSciNet
  2. V. Lakshmikantham, S. Leela, and F. A. McRae, “Improved generalized quasilinearization (GQL) method,” Nonlinear Analysis: Theory, Methods & Applications, vol. 24, no. 11, pp. 1627–1637, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. J. Henderson, Boundary Value Problems for Functional-Differential Equations, World Scientific, River Edge, NJ, USA, 1995. View at MathSciNet
  4. D. Jiang, M. Fan, and A. Wan, “A monotone method for constructing extremal solutions to second-order periodic boundary value problems,” Journal of Computational and Applied Mathematics, vol. 136, no. 1-2, pp. 189–197, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. M. Sockol and A. S. Vatsala, “A unified exhaustive study of monotone iterative method for initial value problems,” Nonlinear Studies, vol. 8, pp. 429–438, 2004. View at Google Scholar
  6. C. P. Gupta, “A Dirichlet type multi-point boundary value problem for second order ordinary differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 26, no. 5, pp. 925–931, 1996. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. D. Jiang and J. Wei, “Monotone method for first- and second-order periodic boundary value problems and periodic solutions of functional differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 50, no. 7, pp. 885–898, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. T. Jankowski, “Advanced differential equations with nonlinear boundary conditions,” Journal of Mathematical Analysis and Applications, vol. 304, no. 2, pp. 490–503, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. J. Nieto and R. Rodríguez-López, “Existence and approximation of solutions for nonlinear functional differential equations with periodic boundary value conditions,” Computers & Mathematics with Applications, vol. 40, no. 4-5, pp. 433–442, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. J. Nieto and R. Rodríguez-López, “Remarks on periodic boundary value problems for functional differential equations,” Journal of Computational and Applied Mathematics, vol. 158, no. 2, pp. 339–353, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. Z. He and X. He, “Periodic boundary value problems for first order impulsive integro-differential equations of mixed type,” Journal of Mathematical Analysis and Applications, vol. 296, no. 1, pp. 8–20, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. F. Zhang, A. Zhao, and J. Yan, “Monotone iterative method for differential equations with piecewise constant arguments,” Indian Journal of Pure and Applied Mathematics, vol. 31, no. 1, pp. 69–75, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Q. Yao, “Monotone iterative technique and positive solutions of Lidstone boundary value problems,” Applied Mathematics and Computation, vol. 138, no. 1, pp. 1–9, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. T. Jankowski, “Ordinary differential equations with nonlinear boundary conditions of anti-periodic type,” Computers & Mathematics with Applications, vol. 47, no. 8-9, pp. 1429–1436, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. W. Ding, J. Mi, and M. Han, “Periodic boundary value problems for the first order impulsive functional differential equations,” Applied Mathematics and Computation, vol. 165, no. 2, pp. 433–446, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. G. Infante and J. R. L. Webb, “Three-point boundary value problems with solutions that change sign,” Journal of Integral Equations and Applications, vol. 15, no. 1, pp. 37–57, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. P. W. Eloe and L. Zhang, “Comparison of Green's functions for a family of multipoint boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 246, no. 1, pp. 296–307, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. S. A. Marano, “A remark on a second-order three-point boundary value problem,” Journal of Mathematical Analysis and Applications, vol. 183, no. 3, pp. 518–522, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. T. Jankowski, “Solvability of three point boundary value problems for second order differential equations with deviating arguments,” Journal of Mathematical Analysis and Applications, vol. 312, no. 2, pp. 620–636, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. Y. Liu, “Non-homogeneous boundary-value problems of higher order differential equations with p-Laplacian,” Electronic Journal of Differential Equations, vol. 2008, no. 20, pp. 1–43, 2008. View at Google Scholar · View at MathSciNet
  21. Y. Liu, “Positive solutions of mixed type multi-point non-homogeneous BVPs for p-Laplacian equations,” Applied Mathematics and Computation, vol. 206, no. 2, pp. 796–805, 2008. View at Publisher · View at Google Scholar · View at MathSciNet