Abstract
The existence of positive solutions for boundary value problems of nonlinear functional difference equations with-Laplacian operator is investigated. Sufficient conditions are obtained for the existence of at least one positive solution and two positive solutions.
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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/S0002-9939-1994-1204373-9
Grimm LJ, Schmitt K: Boundary value problems for differential equations with deviating arguments. Aequationes Mathematicae 1970,4(1–2):176–190. 10.1007/BF01817758
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)90009-5
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)00120-0
Weng PX, Tian Y: Existence of positive solution for singular
conjugate boundary value problem with delay. Far East Journal of Mathematical Sciences 1999,1(3):367–382.
Wong F-H: Existence of positive solutions for
-Laplacian boundary value problems. Applied Mathematics Letters 1999,12(3):11–17. 10.1016/S0893-9659(98)00164-5
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.
Weng PX, Guo ZH: Existence of positive solutions to BVPs for a nonlinear functional difference equation with
-Laplacian operator. Acta Mathematica Sinica 2006,49(1):187–194.
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.1996.0137
Guo DJ: Nonlinear Functional Analysis. Shandong Scientific Press, **an, China; 1985.
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Yang, S., Shi, B. & Zhang, D. Existence of Positive Solutions for Boundary Value Problems of Nonlinear Functional Difference Equation with -Laplacian Operator.
Bound Value Probl 2007, 038230 (2007). https://doi.org/10.1155/2007/38230
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DOI: https://doi.org/10.1155/2007/38230