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Báo cáo hóa học: " Research Article Existence of Symmetric Positive Solutions for an m-Point Boundary Value Problem"

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 Symmetric Positive Solutions for an m-Point Boundary Value Problem | Hindawi Publishing Corporation Boundary Value Problems Volume 2007 Article ID 79090 14 pages doi 10.1155 2007 79090 Research Article Existence of Symmetric Positive Solutions for an m-Point Boundary Value Problem Yongping Sun and Xiaoping Zhang Received 23 June 2006 Revised 17 December 2006 Accepted 11 March 2007 Recommended by Colin Rogers We study the second-order m-point boundary value problem u t a t f t u t 0 0 t 1 u 0 u 1 y m -2a.iu ni where 0 n1 n2 nm-2 1 2 ai 0 for i 1 2 . m - 2 with y m y12ai 1 m 3. a 0 1 0 to is continuous symmetric on the interval 0 1 and maybe singular at t 0 and t 1 f 0 1 X 0 to 0 to is continuous and f x is symmetric on the interval 0 1 for all x e 0 to and satisfies some appropriate growth conditions. By using Krasnoselskii s fixed point theorem in a cone we get some existence results of symmetric positive solutions. Copyright 2007 Y. Sun and X. Zhang. 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 m-point boundary value problems for ordinary differential equations arise in a variety of different areas of applied mathematics and physics. In the past few years the existence of positive solutions for nonlinear second-order multipoint boundary value problems has been studied by many authors by using the Leray-Schauder continuation theorem nonlinear alternative of Leray Schauder coincidence degree theory Krasnosel-skii s fixed point theorem Leggett-Wiliams fixed point theorem or lower- and uppersolutions method see 1-21 and references therein . On the other hand there is much current attention focusing on questions of symmetric positive solutions for second-order two-pointboundary value problems for example Avery and Henderson 22 Henderson and Thompson 23 imposed conditions on f to yield at least three symmetric positive solutions to the problem y f y 0 0 .