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 and Uniqueness of Positive Solutions for Discrete Fourth-Order Lidstone Problem with a Parameter | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 97i540 18 pages doi 2010 971540 Research Article Existence and Uniqueness of Positive Solutions for Discrete Fourth-Order Lidstone Problem with a Parameter Yanbin Sang 1 2 Zhongli Wei 2 3 and Wei Dong4 1 Department of Mathematics North University of China Taiyuan Shanxi 030051 China 2 School of Mathematics Shandong University Jinan Shandong 250100 China 3 Department of Mathematics Shandong Jianzhu University Jinan Shandong 250101 China 4 Department of Mathematics Hebei University of Engineering Handan Hebei 056021 China Correspondence should be addressed to Yanbin Sang sangyanbin@ Received 9 January 2010 Revised 23 March 2010 Accepted 26 March 2010 Academic Editor A. Pankov Copyright 2010 Yanbin Sang 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. This work presents sufficient conditions for the existence and uniqueness of positive solutions for a discrete fourth-order beam equation under Lidstone boundary conditions with a parameter the iterative sequences yielding approximate solutions are also given. The main tool used is monotone iterative technique. 1. Introduction In this paper we are interested in the existence uniqueness and iteration of positive solutions for the following nonlinear discrete fourth-order beam equation under Lidstone boundary conditions with explicit parameter p given by à4y t - 2 - pA2y t - 1 h 0 f1 y 0 2 y t t e a 1 b - 1 z 1-1 y a 0 A2y a - 1 y b 0 A2y b - 1 L2 where A is the usual forward difference operator given by Ay t y f 1 - y t A y t A -1 Ay t c d Z c c 1 . d - 1 d and p 0 is a real parameter. In recent years the theory of nonlinear difference equations has been widely applied to many fields such as economics neural network ecology and cybernetics for details see
