权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Oscillatory properties of solutions of higher order differential equations

高阶微分方程解的振荡特性

基本信息

批准号：
11640170
负责人：
NAITO Manabu
金额：
$ 2.05万
依托单位：
EHIME UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640170/
关键词：
oscillation positive solution half-linear eigenvalue problem singular boundary value problem 境界値問題

项目摘要

The aim of this research is to investigate the oscillatory properties of solutions of higher-order (including second-order) ordinary differential equations of the Emden-Fowler type, and to investigate the oscillatory properties of solutions of elliptic differential equations on the base of the results for ordinary differential equations.The new results and knowledge obtained in the two years are as follows :1. For the second-order half-linear ordinary differential equations, a generalization and an analogue of the Sturm-Liouville linear regular eigenvalue problem are obtained.2. For the four-dimensional Emden-Fowler differential systems, a complete characterization for the existence of nonoscillatory solutions with specific asymptotic properties as t→∞ is established, and a characterization for the nonexistence of nonoscillatory solutions is also obtained.3. For higher-order ordinary differential equations with general nonlinearities, a characterization for the existence of nonoscillatory solutions of the Kiguradze classes is established.4. For a singular eigenvalue value problem to higher-order linear ordinary differential equations, it is shown that there is a countable sequence of eigenvalues and that the n-th eigenfunction has exactly n zeros in an infinite interval under consideration.5. For the second-order quasilinear ordinary differential equations, the asymptotic forms of positive solutions are completely determined.6. For the second-order quasilinear elliptic differential equations, a sufficient condition for the oscillation of all solutions is established.7. For the two-dimensional semilinear elliptic differential systems of the Laplace type, an analogue of the Liouville theorem is established.

本研究的目的是研究Emden-Fowler型高阶（包括二阶）常微分方程解的振动性质，并在常微分方程结果的基础上研究椭圆型微分方程解的振动性质。在这两年中获得的新成果和新知识如下：1。对于二阶半线性常微分方程，得到了Sturm-Liouville线性正则特征值问题的一种推广和模拟。对于四维Emden-Fowler微分系统，建立了t→∞时具有特定渐近性质的非振荡解的存在性的完整刻画，并得到了非振荡解的不存在性的一个刻画。3 .对于具有一般非线性的高阶常微分方程，建立了Kiguradze类非振荡解存在性的一个刻画。对于一类高阶线性常微分方程的奇异特征值问题，证明了存在一个可数的特征值序列，并且在考虑的无限区间内，第n个特征函数恰好有n个零。对于二阶拟线性常微分方程，完全确定了正解的渐近形式。对于二阶拟线性椭圆型微分方程，建立了其所有解振动的充分条件。对于Laplace型二维半线性椭圆型微分系统，建立了一个类似于Liouville定理的方法。