{"title":"Existence of Positive Solutions for Second-Order Difference Equation with Discrete Boundary Value Problem","authors":"Thanin Sitthiwirattham, Jiraporn Reunsumrit","volume":89,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":816,"pagesEnd":822,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/9998364","abstract":"
We study the existence of positive solutions to the three
\r\npoints difference-summation boundary value problem. We show the
\r\nexistence of at least one positive solution if f is either superlinear or
\r\nsublinear by applying the fixed point theorem due to Krasnoselskii
\r\nin cones.<\/p>\r\n","references":"[1] V. A. Ilin and E. I. Moiseev, Nonlocal boundary-value problem of the\r\nfirst kind for a Sturm-Liouville operator in its differential and finite\r\ndifference aspects, J. Differential Equations 23(1987), 803-810.\r\n[2] C. P. Gupta, Solvability of a three-point nonlinear boundary value\r\nproblem for a second order ordinary differential equations, J. Math.\r\nAnal. Appl. 168(1992) no.2, 540-551.\r\n[3] R.P. Agarwal, Focal Boundary Value Problems for Differential and\r\nDifference Equations, Kluwer Academic Publishers, Dordrecht, 1998.\r\n[4] R.P. Agarwal, D. O\u2019Regan, P.J.Y. Wong, Positive Solutions of Differential,\r\nDifference and Integral Equations, Kluwer Academic Publishers,\r\nDordrecht, 1999.\r\n[5] M.A. Krasnoselskii, Positive Solutions of Operator Equations, Noordhoof,\r\nGronignen, 1964.\r\n[6] R.W.Leggett, L.R.Williams, Multiple positive fixed points of nonlinear\r\noperators on ordered Banach spaces. Indiana Univ. Math. J. 28(1979),\r\n673-688.\r\n[7] Z.Bai,X. Liang,Z. Du, Triple positive solutions for some second-order\r\nboundary value problem on a measure chain. Comput. Math. Appl.\r\n53(2007), 1832-1839.\r\n[8] X.He, W. Ge, Existence of three solutions for a quasilinear two-point\r\nboundary value problem. Comput. Math. Appl. 45(2003), 765769.\r\n[9] X. Lin, W. Lin, Three positive solutions of a secound order difference\r\nEquations with Three-Point Boundary Value Problem, J.Appl. Math.\r\nComut. 31(2009), 279-288.\r\n[10] G. Zhang, R. Medina, Three-point boundary value problems for difference\r\nequations, Comp. Math. Appl. 48(2004), 1791-1799.\r\n[11] T. Sitthiwirattham, J. Tariboon, Positive Solutions to a Generalized\r\nSecond Order Difference Equation with Summation Boundary Value\r\nProblem. Journal of Applied Mathematics. Vol.2012, Article ID 569313,\r\n15 pages.\r\n[12] J. Henderson, H.B. Thompson, Existence of multiple solutions for\r\nsecond order discrete boundary value problems, Comput. Math. Appl.\r\n43 (2002), 1239-1248.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 89, 2014"}