Existence of Positive Solutions for Boundary Value Problems of Nonlinear Functional Difference Equation with http://static-content.springer.com/image/art%3A10.1155%2F2007%2F38230/MediaObjects/13661_2007_Article_644_IEq1_HTML.gif -Laplacian Operator

  • SJ Yang1,

    Affiliated with

    • B Shi1Email author and

      Affiliated with

      • DC Zhang1

        Affiliated with

        Boundary Value Problems20072007:038230

        DOI: 10.1155/2007/38230

        Received: 18 March 2007

        Accepted: 23 May 2007

        Published: 14 August 2007


        The existence of positive solutions for boundary value problems of nonlinear functional difference equations with http://static-content.springer.com/image/art%3A10.1155%2F2007%2F38230/MediaObjects/13661_2007_Article_644_IEq2_HTML.gif -Laplacian operator is investigated. Sufficient conditions are obtained for the existence of at least one positive solution and two positive solutions.


        Authors’ Affiliations

        Institute of Applied Mathematics, Naval Aeronautical Engineering Institute


        1. Erbe LH, Wang H: On the existence of positive solutions of ordinary differential equations. Proceedings of the American Mathematical Society 1994,120(3):743–748. 10.1090/S0002-9939-1994-1204373-9MATHMathSciNetView Article
        2. Grimm LJ, Schmitt K: Boundary value problems for differential equations with deviating arguments. Aequationes Mathematicae 1970,4(1–2):176–190. 10.1007/BF01817758MATHMathSciNetView Article
        3. Gustafson GB, Schmitt K: Nonzero solutions of boundary value problems for second order ordinary and delay-differential equations. Journal of Differential Equations 1972,12(1):129–147. 10.1016/0022-0396(72)90009-5MATHMathSciNetView Article
        4. Weng PX, Jiang D: Existence of positive solutions for boundary value problem of second-order FDE. Computers & Mathematics with Applications 1999,37(10):1–9. 10.1016/S0898-1221(99)00120-0MATHMathSciNetView Article
        5. Weng PX, Tian Y: Existence of positive solution for singular http://static-content.springer.com/image/art%3A10.1155%2F2007%2F38230/MediaObjects/13661_2007_Article_644_IEq3_HTML.gif conjugate boundary value problem with delay. Far East Journal of Mathematical Sciences 1999,1(3):367–382.MATHMathSciNet
        6. Wong F-H: Existence of positive solutions for http://static-content.springer.com/image/art%3A10.1155%2F2007%2F38230/MediaObjects/13661_2007_Article_644_IEq4_HTML.gif -Laplacian boundary value problems. Applied Mathematics Letters 1999,12(3):11–17. 10.1016/S0893-9659(98)00164-5MATHMathSciNetView Article
        7. Yang SJ, Shi B, Gai MJ: Boundary value problems for functional differential systems. Indian Journal of Pure and Applied Mathematics 2005,36(12):685–705.MATHMathSciNet
        8. Weng PX, Guo ZH: Existence of positive solutions to BVPs for a nonlinear functional difference equation with http://static-content.springer.com/image/art%3A10.1155%2F2007%2F38230/MediaObjects/13661_2007_Article_644_IEq5_HTML.gif -Laplacian operator. Acta Mathematica Sinica 2006,49(1):187–194.MATHMathSciNetView Article
        9. Ntouyas SK, Sficas YG, Tsamatos PCh: Boundary value problems for functional-differential equations. Journal of Mathematical Analysis and Applications 1996,199(1):213–230. 10.1006/jmaa.1996.0137MATHMathSciNetView Article
        10. Guo DJ: Nonlinear Functional Analysis. Shandong Scientific Press, Jinan, China; 1985.


        © S. J. Yang et al. 2007

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