变系数四阶边值问题正解存在性

变系数四阶边值问题正解存在性

Existence of Positive Solutions for Fourth-Order Boundary

Value Problem with Variable Coefficients

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数学物理学报

柴国庆;黄朝炎

湖北师范学院数学系黄石 435002

收稿日期:2005-08-18 修回日期:2006-10-24 出版日期:2007-12-25 发布日期:2007-12-25
通讯作者: 柴国庆
基金资助:
湖北省教育厅重点项目(D200722002)资助

Chai Guoqing;Huang Chaoyan

Department of Mathematics, Hubei Normal University, Huangshi 435002

Received:2005-08-18 Revised:2006-10-24 Online:2007-12-25 Published:2007-12-25
Contact: Chai Guoqing

摘要： 该文结合算子谱论,应用锥不动点定理,建立了四阶边值问题

$\left\{ {\begin{array}{l}u^{(4)} + B(t){u}'' - A(t)u = f(t,u),0 < t < 1 ,\\u(0) = u(1) = {u}''(0) = {u}''(1) = 0 \end{array}} \right.$
正解存在性定理,这里

$A(t),B(t) \in C[0,1]$ ,

$f(t,u):[0,1]\times [0,\infty ) \to [0,\infty )$ 连续.

关键词: 正解, 不动点定理, 算子谱

Abstract: In this paper, by use of the fixed point
theorem, combining spectral theory of operator, the authors
establish the theorem on existence of positive solutions for
fourth-order boundary value problem with variable coefficient as
follows

$\left\{ {\begin{array}{l} u^{(4)} + B(t){u}'' - A(t)u = f(t,u),0 < t < 1 ,\\ u(0) = u(1) = {u}''(0) = {u}''(1) = 0 \end{array}} \right.$
\noindent where

$A(t),B(t) \in C[0,1]$ and

$f(t,u):[0,1]\times [0,\infty ) \to[0,\infty )$ is continuous.

Key words: Positive solutions, Fixed point theorem, Operator spectra

中图分类号:

34B15

柴国庆;黄朝炎. 变系数四阶边值问题正解存在性[J]. 数学物理学报, 2007, 27(6): 1065-1073.

Chai Guoqing;Huang Chaoyan.

Existence of Positive Solutions for Fourth-Order Boundary

Value Problem with Variable Coefficients

[J]. Acta mathematica scientia,Series A, 2007, 27(6): 1065-1073.

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