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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 for Nonlocal Fourth-Order Boundary Value Problem with Variable Parameter | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 604046 11 pages doi 10.1155 2011 604046 Research Article Existence of Positive Solutions for Nonlocal Fourth-Order Boundary Value Problem with Variable Parameter Xiaoling Han Hongliang Gao and Jia Xu Department of Mathematics Northwest Normal University Lanzhou 730070 China Correspondence should be addressed to Xiaoling Han hanxiaoling@nwnu.edu.cn Received 26 November 2010 Accepted 14 January 2011 Academic Editor M. Furi Copyright 2011 Xiaoling Han 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. By using the Krasnoselskii s fixed point theorem and operator spectral theorem the existence of positive solutions for the nonlocal fourth-order boundary value problem with variable parameter u t B f u f Xf t u t u t 0 t 1 u 0 m 1 Jq p s u s ds u 0 u 1 J0 q s u s ds is considered where p q e L1 0 1 X 0 is a parameter and B e C 0 1 f e C 0 1 X 0 to X -TO 0 0 to . 1. Introduction The existence of positive solutions for nonlinear fourth-order multipoint boundary value problems has been studied by many authors using nonlinear alternatives of Leray-Schauder the fixed point theory and the method of upper and lower solutions see e.g. 1-15 and references therein . The multipoint boundary value problem is in fact a special case of the boundary value problem with integral boundary conditions. Recently Bai 16 studied the existence of positive solutions of nonlocal fourth-order boundary value problem u 4 t pu t Xf t u t u t 0 t 1 u 0 u 1 p s u s ds 0 f1 u 0 u 1 q s u s ds. 0 1.1 2 Fixed Point Theory and Applications under the assumption A1 A 0 and 0 p n2 A2 f e C 0 1 X 0 to X -TO 0 0 to p q e L1 0 1 p s 0 q s 0 0 p s ds 1 Jq1 q s sin y psds J1 q s sin vp 1 - s ds sin ựp. In this paper we study the above generalizing form with .
