Research Article | Open Access

Huting Yuan, Guang Zhang, Hongliang Zhao, "Existence of Positive Solutions for a Discrete Three-Point Boundary Value Problem", *Discrete Dynamics in Nature and Society*, vol. 2007, Article ID 049293, 14 pages, 2007. https://doi.org/10.1155/2007/49293

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

#### Abstract

A discrete three-point boundary value problem

#### References

- 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 - 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 Site | Google Scholar | Zentralblatt MATH | MathSciNet - 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 Site | Google Scholar | Zentralblatt MATH | MathSciNet - 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 Site | Google Scholar | Zentralblatt MATH | MathSciNet - 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 Site | Google Scholar | Zentralblatt MATH | MathSciNet - 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: Google Scholar | Zentralblatt MATH | MathSciNet - 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 Site | Google Scholar | Zentralblatt MATH | MathSciNet - 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 Site | Google Scholar | Zentralblatt MATH | MathSciNet - 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 | Zentralblatt MATH | MathSciNet - 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 | Zentralblatt MATH | MathSciNet - 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 Site | Google Scholar | Zentralblatt MATH | MathSciNet - J. Henderson, “Positive solutions for nonlinear difference equations,”
*Nonlinear Studies*, vol. 4, no. 1, pp. 29–36, 1997. View at: Google Scholar | Zentralblatt MATH | MathSciNet - 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 | MathSciNet - 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 | Zentralblatt MATH | MathSciNet - 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 | Zentralblatt MATH | MathSciNet - 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 Site | Google Scholar | Zentralblatt MATH | MathSciNet - P. J. Y. Wong, “Positive solutions of discrete $\left(n,p\right)$ boundary value problems,”
*Nonlinear Analysis. Theory, Methods & Applications*, vol. 30, no. 1, pp. 377–388, 1997. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet - 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 Site | Google Scholar | Zentralblatt MATH | MathSciNet - 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 Site | Google Scholar | Zentralblatt MATH | MathSciNet - M. A. Krasnosel'skiĭ,
*Positive Solutions of Operator Equations*, P. Noordhoff, Groningen, The Netherlands, 1964. View at: Zentralblatt MATH | MathSciNet - 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 | MathSciNet - D. J. Guo,
*Nonlinear Functional Analysis*, The Science and Technology Press, Shandong, China, 1985.

#### Copyright

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.