tailieunhanh - Báo cáo hóa học: " Research Article Existence of Positive Solutions for Fourth-Order Three-Point Boundary Value Problems Chuanzhi Bai"

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 Fourth-Order Three-Point Boundary Value Problems Chuanzhi Bai | Hindawi Publishing Corporation Boundary Value Problems Volume 2007 Article ID 68758 10 pages doi 2007 68758 Research Article Existence of Positive Solutions for Fourth-Order Three-Point Boundary Value Problems Chuanzhi Bai Received 11 July 2007 Accepted 7 November 2007 Recommended by Jean Mawhin We are concerned with the nonlinear fourth-order three-point boundary value problem u 4 t a t f u t 0 t 1 u 0 u 1 0 au n - hu n 0 yu 1 ổu 1 0. By using Krasnoselskii s fixed point theorem in a cone we get some existence results of positive solutions. Copyright 2007 Chuanzhi Bai. 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 As is pointed out in 1 2 boundary value problems for second- and higher-order differential equations play a very important role in both theory and applications. Recently an increasing interest in studying the existence of solutions and positive solutions to boundary value problems for fourth-order differential equations is observed see for example 3-8 . In this paper we are concerned with the existence of positive solutions for the following fourth-order three-point boundary value problem BVP u 4 t a t f u t 0 t 1 u 0 u 1 0 au n pu n 0 yu 1 ổu 1 0 where a p y and s are nonnegative constants satisfying aS Py ay 0 0 n 1 a e C 0 1 and f e C 0 oo 0 oo . We use Krasnoselskii s fixed point theorem in cones to establish some simple criteria for the existence of at least one positive solution to BVP . To the best of our knowledge no paper in the literature has investigated the existence of positive solutions for BVP . 2 Boundary Value Problems The paper is formulated as follows. In Section 2 some definitions and lemmas are given. In Section 3 we prove some existence theorems of the positive solutions for BVP . 2. Preliminaries and lemmas In this section we .