非线性三阶差分方程三点特征值问题的正解

Positive Solutions to Three-Point Eigenalue Problems for Nonlinear Third-Order Difference Equations

作者：耿天梅(西北师范大学数学与统计学院)；高承华(西北师范大学数学与统计学院)；王燕霞(西北师范大学数学与统计学院)

Author：GENG Tian-Mei(College of Mathematics and Statistics, Northwest Normal University)；GAO Cheng-Hua(College of Mathematics and Statistics, Northwest Normal University)；WANG Yan-Xia(College of Mathematics and Statistics, Northwest Normal University)

收稿日期：2016-01-09 年卷（期）页码：2016,53(6):1215-1221

期刊名称：四川大学学报: 自然科学版

Journal Name：Journal of Sichuan University (Natural Science Edition)

关键字：非线性三阶差分方程，三点特征值问题，正解，锥，不动点定理

Key words：Nonlinear third-order difference equation, three-point boundary value problem, positive solution, cone, fixed point theorem.

基金项目：中国博士后基金,省自然科学基金,其它

中文摘要

在本文中,通过使用锥不动点定理,我们得到离散非线性三阶三点特征值问题的正解的存在 △3u(t-1)= λa(t)f(t,u(t)),t∈[1,T]Z, u(0)=△u(?)=△u(T)=0, 这里 ?∈[[(T2+T)/(3T+2)]+1,T]Z,和λ>0 是一个参数.

英文摘要

In this paper, by using the fixed point theorem in cone, we obtain the existence of positive solutions to the discrete nonlinear third-order three-point eigenvalue problem △3u(t-1)= λa(t)f(t,u(t)),t∈[1,T]Z, u(0)=△u(?)=△u(T)=0, where ?∈[[(T2+T)/(3T+2)]+1,T]Z, and λ>0 is a parameter.

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论文摘要

非线性三阶差分方程三点特征值问题的正解

Positive Solutions to Three-Point Eigenalue Problems for Nonlinear Third-Order Difference Equations