一类奇异的三阶三点非齐次边值问题的正解  

Positive solutions for a class of third order three point nonhomogeneous boundary value problems

作　　者：何希萍[1] 孙红蕊[2] 

机构地区：[1]甘肃广播电视大学教学指导中心,兰州730030 [2]兰州大学数学与统计学院,兰州730000

出　　处：《兰州大学学报（自然科学版）》2011年第3期81-85,共5页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金项目(10801065);兰州大学中央高校基本科研业务费专项基金项目(LZUJBKY-2011-43)

摘　　要：研究了一类奇异的三阶非线性常微分方程三点非齐次边值问题.运用不动点指数理论,在适当假设下,证明了当非线性项f为超线性时,该问题对小的正参数b至少有一个正解,当b足够大时,该问题没有正解;而当f为次线性时,该问题对所有的正参数b都有正解.A class of singular third order nonlinear ordinary differential equations with three point nonhomogeneous boundary value conditions were investigated. By using the fixed point index theory and under suitable hypothesis, it was shown that when the nonlinearity f is superlinear, the problem has at least one solution if the parameter b is small enough, and the problem has no positive solution if b is large enough. When f is sublinear, the problem has at least one positive solution for every b 〉 0.

关 键 词：三阶三点边值问题 非齐次 正解 存在性 不动点指数 

分 类 号：O175.14[理学—数学]