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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 Solutions for Singular Higher Order Continuous and Discrete Boundary | Hindawi Publishing Corporation Boundary Value Problems Volume 2008 Article ID 123823 11 pages doi 10.1155 2008 123823 Research Article Existence and Uniqueness of Solutions for Singular Higher Order Continuous and Discrete Boundary Value Problems Chengjun Yuan 1 2 Daqing Jiang 1 and You Zhang1 1 School of Mathematics and Statistics Northeast Normal University Changchun 130024 Jilin China 2 School of Mathematics and Computer Harbin University Harbin 150086 Heilongjiang China Correspondence should be addressed to Chengjun Yuan ycj7102@163.com Received 4 July 2007 Accepted 31 December 2007 Recommended by Raul Manasevich By mixed monotone method the existence and uniqueness are established for singular higher-order continuous and discrete boundary value problems. The theorems obtained are very general and complement previous known results. Copyright 2008 Chengjun Yuan 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 the study of higher-order continuous and discrete boundary value problems has been studied extensively in the literature see 1-17 and their references . Most of the results told us that the equations had at least single and multiple positive solutions. Recently some authors have dealt with the uniqueness of solutions for singular higher-order continuous boundary value problems by using mixed monotone method for example see 6 14 15 . However there are few works on the uniqueness of solutions for singular discrete boundary value problems. In this paper we state a unique fixed point theorem for a class of mixed monotone operators see 6 14 18 . In virtue of the theorem we consider the existence and uniqueness of solutions for the following singular higher-order continuous and discrete boundary value problems 1.1 and 1.2 by using mixed monotone method. We first .
