摘要
考察了一类奇异四阶两点边值问题的正解,其中允许非线性项奇异.主要工具是全连续算子的逼近定理和锥拉伸与锥压缩型的Guo-Krasnosel’skii不动点定理.在力学上这一类问题描述了两端刚性固定的弹性梁的形变.为了描述非线性项的增长,引入了非线性项的主要部分和高度函数.结果表明只要在某些有界集合上的主要部分的高度和高度函数的积分是适当的,该类问题可以具有n个正解,其中n是一个任意的正整数.
We consider the positive solutions to a class of nonlinear fourth-order two-point boundary value problems, where the nonlinear term is allowed to be singular. Main foundation is the approximation theorem of completely continuous operators and the Guo-Krasnosel＇skii fixed point theorem of cone expansion-compression type. In mechanics, this class of problems describe the deformation of an elastic beam rigidly fixed at both ends. In order to describe the growth of nonlinear term we introduce the principal and singular parts of nonlinear term. The results show that this class of problems can have n positive solutions provided the heights of principal part and the integrations of height function on some bounded sets are appropriate, where n is an arbitrary positive integer.
出处
《武汉大学学报（理学版）》
CAS
CSCD
北大核心
2009年第2期129-133,共5页
Journal of Wuhan University:Natural Science Edition
基金
国家自然科学基金资助项目(10571085)
关键词
奇异常微分方程
边值问题
正解
存在性
多解性
singular ordinary differential equation
boundary value problem
positive solution
existence
multiplicity
