tailieunhanh - báo cáo hóa học:" Research Article Unbounded Solutions of Second-Order Multipoint Boundary Value Problem on the Half-Line"

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 Unbounded Solutions of Second-Order Multipoint Boundary Value Problem on the Half-Line | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 236560 15 pages doi 2010 236560 Research Article Unbounded Solutions of Second-Order Multipoint Boundary Value Problem on the Half-Line Lishan Liu 1 2 Xinan Hao 1 and Yonghong Wu2 1 School of Mathematical Sciences Qufu Normal University Qufu 273165 Shandong China 2 Department of Mathematics and Statistics Curtin University of Technology Perth WA 6845 Australia Correspondence should be addressed to Lishan Liu lls@ Received 14 May 2010 Revised 4 September 2010 Accepted 11 October 2010 Academic Editor Vicentiu Radulescu Copyright 2010 Lishan Liu 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 paper investigates the second-order multipoint boundary value problem on the half-line u t f t u t u t 0 t e R au 0 - fu 0 - 2 1 kiu Ềf a 0 limt TOu t b 0 where a 0 f 0 ki 0 0 ềi TO ụ 1 2 . n and f R X R X R R is continuous. We establish sufficient conditions to guarantee the existence of unbounded solution in a special function space by using nonlinear alternative of Leray-Schauder type. Under the condition that f is nonnegative the existence and uniqueness of unbounded positive solution are obtained based upon the fixed point index theory and Banach contraction mapping principle. Examples are also given to illustrate the main results. 1. Introduction In this paper we consider the following second-order multipoint boundary value problem on the half-line u f f t u t u t 0 t e R n au 0 - fu 0 - y kiuftf a 0 lim u f b 0 t TO i 1 where a 0 f 0 ki 0 0 ị1 ị2 ịn TO and f R X R X R R is continuous in which R 0 to R -TO to . The study of multipoint boundary value problems BVPs for second-order differential equations was initiated by Bicadze and Samarskl 1 and later continued by Il in and 2 Boundary Value .