Positive Solutions for Discrete Third-order Three-point Boundary Value Problem

Authors: Benshi Zhu

Abstract:

In this paper, the existence of multiple positive solutions for a class of third-order three-point discrete boundary value problem is studied by applying algebraic topology method.

Keywords: Positive solutions, Discrete boundary value problem, Third-order, Three-point, Algebraic topology

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334341

References:

[1] R. P. Agarwal, D. O'Regan, "Multiple solutions for higher order difference equations," Comput. Math. Appl., vol. 37, no. 9, pp. 39-48, May 1999.
[2] R. P. Agarwal, F.H.Wong, "Existence of positive solution for higher order difference equations," Appl. Math. Lett., vol. 10, no. 5, pp. 67-74, Sep.1997.
[3] D.R. Anderson, R.I. Avery, "Multiple positive solutions to a third-order discrete focal boundary value problem," Comput. Math. Appl., vol. 42, no. 3-5, pp. 333-340, Aug.-Sep. 2001
[4] D.R. Anderson, "Discrete third-order three-point right focal boundary value problem," Comput. Math. Appl., vol. 45, no. 6-9, pp. 861-871, Mar.-May 2003
[5] Z.J. Du, "Positive solutions for a second-order three-point discrete boundary value problem," J. Appl. Math. Comput., vol. 26, no. 1-2, pp. 219-231, Jan.. 2008.
[6] I.Y. Karaca, "Discrete third-order three-point boundary value problem," J. Comput. Appl. Math., vol. 205, no. 1, pp. 458-468, Aug. 2007
[7] X.J. Lin, W.B. Liu, "Three positive solutions for a second order difference equation with three-point boundary value problem," J. Appl. Math. Comput., vol. 31, no. 1-2, pp. 279-288, Jan. 2009.
[8] R.Y. Ma, Y.N. Raffoul, "Positive Solutions of Three-point Nonlinear Discrete Second Order Boundary Value Problem," J. Diff. Eqns Appl.., vol. 10, no. 4, pp. 129-138, Apr. 2004.
[9] F.H. Wong, R.G. Agarwal, "Double positive solutions of $(n,p)$ boundary value problems for higher order difference equations," Comput. Math. Appl., vol. 32, no. 8, pp. 1-21, Oct. 1996.
[10] S.H. Wu, "The existence of multiple solutions to differential equation and difference equaiton(in Chinese)," Chinese J. Engineering Math., vol. 26, no. 4, pp. 895-905, Apr. 2009.
[11] C.M. Yang, P.X. Weng, "Green function and positive solutions for boundary value problems of third-order difference equaitons," Comput. Math. Appl., vol. 54, no. 4, pp. 567-578, Aug. 2007.
[12] G. Zhang, R. Medina, "Three-point boundary value problems for difference equations," Comput. Math. Appl., vol. 48, no. 12, pp. 1791-1799, Dec. 2004.
[13] G. Zhang, Z. Yang, "Positive solutions of a general discrete boundary value problem," J. Math. Anal. Appl., vol. 339, no. 1, pp. 469-481, Mar. 2008.