Research on Global Properties and Correlation of Solutions to Functioanl Equations and Difference Equations

函数方程和差分方程解的全局性质及相关性研究

基本信息

批准号：
14540158
负责人：
NAITO Toshiki
金额：
$ 2.62万
依托单位：
The University of Electro-Communications
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2003
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540158/
关键词：
Linear Differential Equations Linear Difference Equations Bounded Solutions Almost Periodic Solutions Variation of Constants Formula Fundamental Solution Method Voice generation Population Dynamics 周期線形微分方程式周期写像初期値問題周期解周期線形関数微分

项目摘要

1.The existence conditions of bounded solutions of the linear differential equation with a periodic forcing function are obtained by using the difference equations. The itteration of the period solution map makes a sequence which is a solutions of a linear difference equation. The general term of this sequence is represented by the initial term, the mean of the periodic forcing function and the eigenvalues of the coefficient matrix. The boundedness and periodicity of solutions are determined completely by initial values ant the mean of the forcing functions. 2.Linear functional differential equations in a Banach space are transformed to opertor equations on the space of bounded continuous functions. The spectrum of the solutions are computed and the existence of solutions whose spectrum satisfies the period conditions are computed and the existence of solutions whose spectrum satisfies the period conditions are obtained. 3.The general variation of constants formula is completely obtain … More ed on the phase space for linear periodic functional differential equations. The formula is applied for the existence of periodic solutions. 4.Analytic solutions of difference equations are applied to the research in the population and environmental sciences. 5.The numerical simulation algorithm is developed based on the finite element method that reduces the radiation and scattering problem in an unbounded region into the one in a bounded region using aritificial boundary. 6.A fundamental solution method applied to reduced wave problems in the exterior domain of disc has been investigated. The case of equi-distant equally phased arrangement of source points and collocation points has been studied from the view points of both theoretical analysis and numerical experiment. 7.Pertabations of eigenvalues are studied for structural-acoustic system. Well-posedness of the Cauchy problem is studied in Gevrey class for some weakly hyperbolic equations of higher order. Fixed point theorems are applied to the stability theory of solutions of integral differential equations. Less

1。iTions。时期映射的序列是线性差异方程的解决方案解决方案是通过Banach空间中的初始竞争力确定的，将解决方案的opertor方程式转换为溶液的范围，并且存在的溶液的存在。 Orula适用于周期性解决方案的存在。外部盘的问题已经研究了源点的相同情况。在Gevrey类中，研究了一些弱叠加的ixed Point定理。