Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2007, Article ID 49293, 14 pages
http://dx.doi.org/10.1155/2007/49293
Research Article

Existence of Positive Solutions for a Discrete Three-Point Boundary Value Problem

1Department of Mathematics, Yanbei Normal University, Datong, Shanxi 037000, China
2School of Science, Tianjin University of Commerce, Tianjin 300134, China
3Department of Mathematics, Qingdao Technological University, 11 Fushun Road, Qingdao 266033, China

Received 26 July 2006; Revised 21 November 2006; Accepted 22 November 2006

Copyright © 2007 Huting Yuan 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. V. A. II'in and E. I. Moiseev, “A nonlocal boundary value problems of the second kind for a Sturm-Liouville operator,” Differential Equations, vol. 23, no. 8, pp. 979–987, 1987. View at Google Scholar
  2. W. Feng and J. R. L. Webb, “Solvability of m-point boundary value problems with nonlinear growth,” Journal of Mathematical Analysis and Applications, vol. 212, no. 2, pp. 467–480, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. W. Feng, “On a m-point boundary value problem,” Nonlinear Analysis. Theory, Methods & Applications, vol. 30, no. 8, pp. 5369–5374, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. C. P. Gupta, “Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation,” Journal of Mathematical Analysis and Applications, vol. 168, no. 2, pp. 540–551, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. C. P. Gupta and S. I. Trofimchuk, “A sharper condition for the solvability of a three-point second order boundary value problem,” Journal of Mathematical Analysis and Applications, vol. 205, no. 2, pp. 586–597, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. C. P. Gupta, “A generalized multi-point boundary value problem for second order ordinary differential equations,” Applied Mathematics and Computation, vol. 89, no. 1–3, pp. 133–146, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. R. Ma, “Existence theorems for a second order m-point boundary value problem,” Journal of Mathematical Analysis and Applications, vol. 211, no. 2, pp. 545–555, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. R. Ma, “Positive solutions for second-order three-point boundary value problems,” Applied Mathematics Letters, vol. 14, no. 1, pp. 1–5, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. R. Ma, “Positive solutions of a nonlinear three-point boundary-value problem,” Electronic Journal of Differential Equations, vol. 1999, no. 34, pp. 1–8, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. Q. Sheng and R. P. Agarwal, “Existence and uniqueness of the solutions of nonlinear n-point boundary value problems,” Nonlinear World, vol. 2, no. 1, pp. 69–86, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. F. Atici and A. Peterson, “Bounds for positive solutions for a focal boundary value problem,” Computers & Mathematics with Applications, vol. 36, no. 10–12, pp. 99–107, 1998, Advances in difference equations, II. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. Henderson, “Positive solutions for nonlinear difference equations,” Nonlinear Studies, vol. 4, no. 1, pp. 29–36, 1997. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. R. P. Agarwal and P. J. Y. Wong, Advanced Topics in Difference Equations, vol. 404 of Mathematics and Its Applications, Kluwer Academic, Dordrecht, The Netherlands, 1997. View at Zentralblatt MATH · View at MathSciNet
  14. F. Merdivenci, “Two positive solutions of a boundary value problem for difference equations,” Journal of Difference Equations and Applications, vol. 1, no. 3, pp. 263–270, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. F. Merdivenci, “Green's matrices and positive solutions of a discrete boundary value problem,” Panamerican Mathematical Journal, vol. 5, no. 1, pp. 25–42, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. D. Anderson, R. Avery, and A. Peterson, “Three positive solutions to a discrete focal boundary value problem,” Journal of Computational and Applied Mathematics, vol. 88, no. 1, pp. 103–118, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. P. J. Y. Wong, “Positive solutions of discrete (n,p) boundary value problems,” Nonlinear Analysis. Theory, Methods & Applications, vol. 30, no. 1, pp. 377–388, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. R. P. Agarwal and R. A. Usmani, “The formulation of invariant imbedding method to solve multipoint discrete boundary value problems,” Applied Mathematics Letters, vol. 4, no. 4, pp. 17–22, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. G. Zhang and R. Medina, “Three-point boundary value problems for difference equations,” Computers & Mathematics with Applications, vol. 48, no. 12, pp. 1791–1799, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. M. A. Krasnosel'skiĭ, Positive Solutions of Operator Equations, P. Noordhoff, Groningen, The Netherlands, 1964. View at Zentralblatt MATH · View at MathSciNet
  21. D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, vol. 5 of Notes and Reports in Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1988. View at Zentralblatt MATH · View at MathSciNet
  22. D. J. Guo, Nonlinear Functional Analysis, The Science and Technology Press, Shandong, China, 1985.