﻿ 一类奇异三阶三点边值问题正解的存在性 Positive Solutions for a Third-Order Three-Point Singular Boundary Value Problem

Vol.05 No.01(2016), Article ID:16964,7 pages
10.12677/AAM.2016.51004

Positive Solutions for a Third-Order Three-Point Singular Boundary Value Problem

Hongping Wu

College of Mathematics and Statistics, Northwest Normal University, Lanzhou Gansu

Received: Feb. 1st, 2016; accepted: Feb. 20th, 2016; published: Feb. 23rd, 2016

ABSTRACT

This paper is concerned with the following nonlinear third-order three-point boundary value problem

where, the nonlinear term may be singular at and. By using fixed- point theorem in cone, the existence of one or two or n positive solutions is obtained with the weaker conditions.

Keywords:Third-Order Three-Point Boundary Value Problem, Singular, Positive Solutions, Fixed-Point Theorem

1. 引言

(1)

2. 预备与引理

(H1)连续且满足，其中满足

(H2)连续。

(H3) 存在两个连续函数，使得

(H4)是一个非降函数，对于任意的

(H5) 对于任意的，其中

(2)

(3)

(Ey)

，则有

，则连续。

1)；或

2)

3. 主要结果

(A1)

(A2)

，进而根据引理

。 (4)

，则，因此

(5)

(B1)

(B2)

。同样的，利用条件及定理1知，问题(1)还有另一个正解

(C1)

(C2)

(D1)

(D2)

Positive Solutions for a Third-Order Three-Point Singular Boundary Value Problem[J]. 应用数学进展, 2016, 05(01): 24-30. http://dx.doi.org/10.12677/AAM.2016.51004

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