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 Positive Solutions of a Singular Nonlinear Boundary Value Problem | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 458015 16 pages doi 2010 458015 Research Article Existence of Positive Solutions of a Singular Nonlinear Boundary Value Problem Ruyun Ma1 and Jiemei Li1 2 1 College of Mathematics and Information Science Northwest Normal University Lanzhou 730070 China 2 The School of Mathematics Physics Software Engineering Lanzhou Jiaotong University Lanzhou 730070 China Correspondence should be addressed to Ruyun Ma ruyunma@ Received 21 May 2010 Accepted 11 August 2010 Academic Editor Vicentiu Radulescu Copyright 2010 R. Ma and J. Li. 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. We are concerned with the existence of positive solutions of singular second-order boundary value problem u t f t u t 0 t e 0 1 m 0 m 1 0 which is not necessarily linearizable. Here nonlinearity f is allowed to have singularities at t 0 1. The proof of our main result is based upon topological degree theory and global bifurcation techniques. 1. Introduction Existence and multiplicity of solutions of singular problem u f t u 0 t e 0 1 u 0 u 1 0 where f is allowed to have singularities at t 0 and t 1 have been studied by several authors see Asakawa 1 Agarwal and O Regan 2 O Regan 3 Habets and Zanolin 4 Xu and Ma 5 Yang 6 and the references therein. The main tools in 1-6 are the method of lower and upper solutions Leray-Schauder continuation theorem and the fixed point index 2 Boundary Value Problems theory in cones. Recently Ma 7 studied the existence of nodal solutions of the singular boundary value problem u ra fi f u 0 t e 0 1 u 0 u 1 0 by applying Rabinowitz s global bifurcation theorem where a is allowed to have singularities at t 0 1 and f is linearizable at 0 as well as at TO. It is the purpose of this paper to study the existence of .
