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 Multiple Positive Solutions of the Singular Boundary Value Problem for Second-Order Impulsive Differential Equations on the Half-Line | Hindawi Publishing Corporation Boundary Value Problems Volume 2o10 Article ID 281908 13 pages doi 2010 281908 Research Article Multiple Positive Solutions of the Singular Boundary Value Problem for Second-Order Impulsive Differential Equations on the Half-Line Jing Xiao 1 Juan J. Nieto 2 and Zhiguo Luo1 1 Department of Mathematics Hunan Normal University Changsha Hunan 410081 China 2 Departamento de Analisis Matemứtico Facultad de Matemứticas Universidad de Santiago de Compostela 15782 Santiago de Compostela Spain Correspondence should be addressed to Zhiguo Luo luozg@ Received 17 November 2009 Revised 22 January 2010 Accepted 21 February 2010 Academic Editor Claudianor Alves Copyright 2010 Jing Xiao 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 uses a fixed point theorem in cones to investigate the multiple positive solutions of a boundary value problem for second-order impulsive singular differential equations on the halfline. The conditions for the existence of multiple positive solutions are established. 1. Introduction Consider the following nonlinear singular Sturm-Liouville boundary value problems for second-order impulsive differential equation on the half-line p t ufty f t u 0 vt e J àu tk Ik u tk k 1 2 . n au 0 - p lim p f u f 0 t 0 fu ỗ lim p f u Jf 0 t x 1 where J 0 to 0 t1 tn J 0 to J J t1 . tn f e C J X J J p e C J J n C1 J J with p 0 on J and Jg 1 p s ds to a p Ỵ ô 0 with p pY aỗ aỵB 0 x 0 in which B t s Jst 1 p ơỴ dơ. àuftk u tk - u ft- 2 Boundary Value Problems where u tt- and u tk are respectively the left and right limits of u f at tk k 1 . n 1 n TO. The theory of singular impulsive differential equations has been emerging as an important area of investigation in recent years. For the theory and classical results we refer the monographs to 1 2
