Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Existence of Positive Solutions for Boundary Value Problems of Nonlinear Functional Difference Equation with p-Laplacian Operator | Hindawi Publishing Corporation Boundary Value Problems Volume 2007 Article ID 38230 12 pages doi 2007 38230 Research Article Existence of Positive Solutions for Boundary Value Problems of Nonlinear Functional Difference Equation with p-Laplacian Operator S. J. Yang B. Shi and D. C. Zhang Received 18 March 2007 Accepted 23 May 2007 Recommended by Raul Manasevich The existence of positive solutions for boundary value problems of nonlinear functional difference equations with p-Laplacian operator is investigated. Sufficient conditions are obtained for the existence of at least one positive solution and two positive solutions. Copyright 2007 S. J. Yang 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. 1. Introduction In recent years boundary value problems of differential and difference equations have been studied widely and there are many excellent results see Erbe and Wang 1 Grimm and Schmitt 2 Gustafson and Schmitt 3 Weng and Jiang 4 Weng and Tian 5 Wong 6 and Yang et al. 7 . Weng and Guo 8 considered two-point boundary value problem of a nonlinear functional difference equation with p-Laplacian operator AOp Ax t r t f xt 0 t e 0 T x0 ọ e c Ax T 1 0 where Op u u p-2u p 1 0 0 0 c ọ ọ e c ọ k 0 k e -T 0 . Ntouyas et al. 9 investigated the existence of solutions of a boundary value problem for functional differential equations x t f t xt x tp t e 0 T a0x0 - a1x 0 0 p0x T fax T A 2 Boundary Value Problems where f 0 T X Cr X R R is a continuous function p e Cr A e R Cr C r 0 R . Let R x I x e R x 0 a b a . b a b a . b - 1 a 00 a a 1 . for a b e N and a b. For T T e N and 0 T T we define Ct I Ọ T 0 R C e Ct I fi 0 fi e T 0 . Then CT and C are both Banach spaces endowed with the max-norm II Ht max k k . ke T 0 For any real function x defined on the interval T T and any t e 0 T we
