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 Solutions for m-point Boundary Value Problems on a Half-Line | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 609143 11 pages doi 2009 609143 Research Article Existence of Solutions for m-point Boundary Value Problems on a Half-Line Changlong Yu Yanping Guo and Yude Ji College of Sciences Hebei University of Science and Technology Shijiazhuang 050018 Hebei China Correspondence should be addressed to Changlong Yu changlongyu@ Received 5 April 2009 Accepted 6 July 2009 Recommended by Paul Eloe By using the Leray-Schauder continuation theorem we establish the existence of solutions for m-point boundary value problems on a half-line X t f t x t x t 0 0 t x x 0 2m12 aix nf limt xft 0 where a e R Xm-2 ai 1 and 0 n1 n2 Hm-2 - are given. Copyright 2009 Changlong Yu 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 Multipoint boundary value problems BVPs for second-order differential equations in a finite interval have been studied extensively and many results for the existence of solutions positive solutions multiple solutions are obtained by use of the Leray-Schauder continuation theorem Guo-Krasnosel skii fixed point theorem and so on for details see 1-4 and the references therein. In the last several years boundary value problems in an infinite interval have been arisen in many applications and received much attention see 5 6 . Due to the fact that an infinite interval is noncompact the discussion about BVPs on the half-line is more complicated see 5-14 and the references therein. Recently in 15 Lian and Ge studied the following three-point boundary value problem x t f t xft x t 0 0 t TO x 0 ax fi lim X f 0 t to 2 Advances in Difference Equations where a e R a 1 and n e 0 x are given. In this paper we will study the following m-point boundary value problems x t f fixity x ty 0 0 t TO m-2 x 0 y
