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四阶差分方程周期解的存在性研究

发表时间:2008-03-15  浏览量:2263  下载量:659
全部作者: 孙启文,周展
作者单位: 广州大学数学与信息科学学院
摘 要: 本文利用临界点理论, 研究如下四阶高维差分方程在不同的次线性条件下周期解的存在性及多重性,得到周期解存在性的几个充分条件。在这里首先建立差分方程的变分泛函,然后将差分方程的周期解的存在性问题转化为相应的泛函的临界点的存在性问题。这在差分方程周期解存在性及边值问题解的存在性的研究中是一种很新的方法,但事实证明这种方法却是很方便很有用的一种工具。本文所得到的结果补充了历来研究中在这方面的空缺,极大的完善了对四阶差分方程周期解的存在性问题的研究。
关 键 词: 应用数学;四阶差分方程;临界点理论; 周期解
Title: The existence of periodic solutions for forth-order sublinear difference equation
Author: SUN Qiwen, ZHOU Zhan
Organization: School of Mathematics and Information Sciences, Guangzhou University
Abstract: This paper mainly concerns with the existence and multiplicity of periodic solutions for the following class of non-linear fourth-order high-dimensional difference equations where the equation satisfies different sublinear conditions. Some new sufficient conditions for the existence of periodic solutions are obtained . The author establishes the corresponding variational functional first, then reduces the problem of finding periodic solutions of difference equations to that of seeking critical points of the functional. This is a very new method in studying the existence of periodic solutions and existence of solutions to boundary value problems, but in fact it is a very convenient and useful method. The results we obtain here reinforce the vacancy and renew the study for the existence of periodic solutions for the fourth-order difference equations.
Key words: applied mathematics; forth-order difference equation; discrete variational principles; periodic solution
发表期数: 2008年7月第5期
引用格式: 孙启文,周展. 四阶差分方程周期解的存在性研究[J]. 中国科技论文在线精品论文,2008,1(5):501-509.
 
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