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báo cáo hóa học:" Research Article Uniqueness and Parameter Dependence of Positive Solution of Fourth-Order Nonhomogeneous BVPs"

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 Uniqueness and Parameter Dependence of Positive Solution of Fourth-Order Nonhomogeneous BVPs | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 106962 9 pages doi 10.1155 2010 106962 Research Article Uniqueness and Parameter Dependence of Positive Solution of Fourth-Order Nonhomogeneous BVPs Jian-Ping Sun and Xiao-Yun Wang Department of Applied Mathematics Lanzhou University of Technology Lanzhou Gansu 730050 China Correspondence should be addressed to Jian-Ping Sun jpsun@lut.cn Received 23 February 2010 Accepted 11 July 2010 Academic Editor Irena Rachunkova Copyright 2010 J.-P. Sun and X.-Y. Wang. 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 investigate the following fourth-order four-point nonhomogeneous Sturm-Liouville boundary value problem ui-i i f t u t e 0 1 au 0 - fuf0 Ằ1 yu 1 ổu 1 Ằ2 au ị1 - bu f1 -X3 cu fị2 du fị2 -X4 where 0 ị1 ị2 1 and Xi i 1 2 3 4 are nonnegative parameters. Some sufficient conditions are given for the existence and uniqueness of a positive solution. The dependence of the solution on the parameters .h i 1 2 3 4 is also studied. 1. Introduction Boundary value problems BVPs for short consisting of fourth-order differential equation and four-point homogeneous boundary conditions have received much attention due to their striking applications. For example Chen et al. 1 studied the fourth-order nonlinear differential equation u 4 f t ù t e 0 1 1.1 with the four-point homogeneous boundary conditions u 0 u 1 0 au ịỉ - bu 1 0 cu ỗ2 du ỗ2 0 1.2 1.3 where 0 ị1 ị2 1. By means of the upper and lower solution method and Schauder fixed point theorem some criteria on the existence of positive solutions to the BVP 1.1 - 1.3 were 2 Boundary Value Problems established. Bai et al. 2 obtained the existence of solutions for the BVP 1.1 - 1.3 by using a nonlinear alternative of Leray-Schauder type. For other related results one can refer to 3-5 and the .