Asymptotic analysis of nonlinear ordinary differential equations and its applications

非线性常微分方程的渐近分析及其应用

• 批准号: 14540177
• 负责人: USAMI Hiroyuki
• 金额: $ 1.86万
• 依托单位: HIROSHIMA UNIVERSITY
• 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 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540177/
• 关键词: oscillation; elliptic partial differential equation; quasilinear; eigenvalue problem; variational problem; polyharmonic function; parabolic partial differential equation; ordinary differential equations; 楕円型編微分方程式; 多重調和関数; 準線形常微分方程式; 漸近的性質; エム

1.We consider second-order quasilinear ordinary differential equations which can be regarded as generalization of the Emden-Fowler equation. We determine asymptotic forms of every positive solutions. We also establish uniqueness of several types of positive solutions.2.We consider elliptic systems of Emden-Fowler type. We establish sufficient conditions for the oscillation of all solutions to the system. When the coefficient functions behave like positive constant multiples of |x|^a, our conditions are best possible in some sense.3.Until now oscillatory properties of second order quasilinear elliptic equations have been studied under several additional assumptions imposed on the nonlinear terms. However, we can establish effective oscillation criteria without doing so. In particular, for autonomous equations we can establish necessary and sufficient conditions for the oscillation of all solutions.4.Eigenvalue problems are studied for second-order semilnear ordinary differential equations, as well as partial differential equations of elliptic type. Asymptotic forms are obtained for variational eigenfunctions and eigenvalues.5.Asymptotic behavior of evetually positive solutions of n-th order quasilinear ordinary differential equations is studied. We establish necessary and sufficient conditions for the existence of eventually positive solutions with specified asymptotic behavior near the infinity.6.Fourth-order quasilinear ordinary differential equations are studied. We can establish necessary and/or sufficient conditions for such equations to have no eventually positive solutions.

1.我们考虑二阶准线性微分方程，可以被视为emden-fowler方程的概括。我们确定每种阳性解决方案的渐近形式。我们还建立了几种类型的阳性解决方案的独特性。2。我们考虑Emden-Fowler类型的椭圆形系统。我们建立了足够的条件，以振荡系统的所有解决方案。当系数函数的行为像| x |^a的正恒定倍数时，我们的条件在某种意义上是最好的。但是，我们可以在不这样做的情况下建立有效的振荡标准。特别是，对于自主方程式，我们可以为所有解决方案的振荡建立必要的条件。4。二阶半月份普通微分方程以及椭圆类型的部分微分方程研究了Eigenvalue问题。为变异征函数和特征值获得了渐近形式。5.研究了第n级quasilIrinear QuasilIrinear普通微分方程的回避阳性溶液的反应行为。我们建立了必要和充分的条件，以实现无穷大附近的指定渐近行为的最终阳性溶液。6。第四阶准线性普通微分方程。我们可以建立必要和/或足够的条件，使这些方程最终没有正面解决方案。

项目成果

Isolated singularities of sub-polyharmonic functions

次多调和函数的孤立奇点

• 发表时间: 2004
• 期刊: Hokkaido Math.J. 33
• 作者: T.Futamura;Y.Mizuta
• 通讯作者: Y.Mizuta

Existence of nonoscillatory solutions to second-order elliptic systems of Emden-Fowler type

Emden-Fowler 型二阶椭圆系统非振荡解的存在性

• 发表时间: 2006
• 期刊: Indiana University Mathematics Journal 55・1
• 作者: Takasi Kusano;and Tomoyuki Tanigawa;Manabu Naito;Manabu Naito;Takasi Kusano;Manabu Naito
• 通讯作者: Manabu Naito

Asymptotic formula for eigenvalues of simple pendulum Problems

单摆问题特征值的渐近公式

• 发表时间: 2004
• 期刊: Asymptotic analysis 40
• 作者: T.Kobayashi;G.Hector;T.Shibata;T.Shibata;T.Shibata;T.Shibata;A.Bi's;T.Kobayashi;T.Shibata;T.Shibata;T.Shibata;T.Shibata
• 通讯作者: T.Shibata

Asymptotic formula foe eigenvalues of simple pendulum problems

简单摆问题特征值的渐近公式

• 发表时间: 2004
• 期刊: Asymptotic Analysis 40
• 作者: Tetsutaro Shibata

Tomomitsu Teramoto: "A Liouvill type theorem for semilinear elliptic systems"Pacific J. Math.. 204. 247-255 (2002)

Tomomitsu Teramoto：“半线性椭圆系统的刘维尔型定理”Pacific J. Math.. 204. 247-255 (2002)