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 The Existence of Countably Many Positive Solutions for Nonlinear nth-Order Three-Point Boundary Value Problems | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 572512 18 pages doi 2009 572512 Research Article The Existence of Countably Many Positive Solutions for Nonlinear nth-Order Three-Point Boundary Value Problems Yude Ji and Yanping Guo College of Sciences Hebei University of Science and Technology Shijiazhuang Hebei 050018 China Correspondence should be addressed to Yude Ji jiyude-1980@ Received 5 July 2009 Revised 30 August 2009 Accepted 30 October 2009 Recommended by Kanishka Perera We consider the existence of countably many positive solutions for nonlinear nth-order three-point boundary value problem u n t a f f u t 0 t e 0 1 u 0 au n u 0 u n-2 0 0 u 1 fu ỳ where n 2 a 0 P 0 0 n 1 a P - a nn-1 1 a t e Lp 0 1 for some p 1 and has countably many singularities in 0 1 2 . The associated Green s function for the nth-order three-point boundary value problem is first given and growth conditions are imposed on nonlinearity f which yield the existence of countably many positive solutions by using the Krasnosel skii fixed point theorem and Leggett-Williams fixed point theorem for operators on a cone. Copyright 2009 Y. Ji and Y. Guo. 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 The existence of positive solutions for nonlinear second-order and higher-order multipoint boundary value problems has been studied by several authors for example see 1-12 and the references therein. However there are a few papers dealing with the existence of positive solutions for the nth-order multipoint boundary value problems with infinitely many singularities. Hao et al. 13 discussed the existence and multiplicity of positive solutions for the following nth-order nonlinear singular boundary value problems u -n f a f f f u 0 t e 0 1 u 0 0 ù 0 u n 2 0 0 u 1 au fi where 0
