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báo cáo hóa học:" Research Article Existence and Uniqueness of Positive Solution for a Singular Nonlinear Second-Order m-Point Boundary Value Problem"

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 Solution for a Singular Nonlinear Second-Order m-Point Boundary Value Problem | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 254928 16 pages doi 10.1155 2010 254928 Research Article Existence and Uniqueness of Positive Solution for a Singular Nonlinear Second-Order m-Point Boundary Value Problem Xuezhe Lv and Minghe Pei Department of Mathematics Beihua University JiLin City 132013 China Correspondence should be addressed to Minghe Pei peiminghe@ynu.ac.kr Received 25 November 2009 Accepted 10 March 2010 Academic Editor Ivan T. Kiguradze Copyright 2010 X. Lv and M. Pei. 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. The existence and uniqueness of positive solution is obtained for the singular second-order m-point boundary value problem u t f t u f 0 for t e 0 1 u 0 0 u 1 2m-2 aiu ni where m 3 ai 0 i 1 2 . m - 2 0 n n2 n.m-1 1 are constants and f t u can have singularities for t 0 and or t 1 and for u 0. The main tool is the perturbation technique and Schauder fixed point theorem. 1. Introduction In this paper we investigate the existence and uniqueness of positive solution for the singular second-order differential equation u t f t u tỴ 0 t e 0 1 with the m-point boundary conditions m-2 u 0 0 u 1 y aiu ni i 1 1.1 1.2 where m 3 ai 0 i 1 2 . m - 2 0 n n2 nm-2 1 are constants and f t u can have singularities for t 0 and or t 1 and for u 0. 2 Boundary Value Problems Multipoint boundary value problems for second-order ordinary differential equations arise in many areas of applied mathematics and physics see 1-3 and references therein. The study of three-point boundary value problems for nonlinear second-order ordinary differential equations was initiated by Lomtatidze 4 5 . Since then the nonlinear second-order multipoint boundary value problems have been studied by many authors see 13 6-29 and references therein. Most of all the works in the above .