Asymptotic Behavior and Periodisity of Solutions of Differdntial Equations

微分方程解的渐近行为和周期性

• 批准号: 63540119
• 负责人: YAMAMOTO Minoru
• 金额: $ 1.15万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1988
• 资助国家: 日本
• 起止时间: 1988 至 1990
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-63540119/
• 关键词: Ordinary Differential Equations; Stability; Asymptotic Behavior; Periodisity; Boundary Value Problems; Oscillation; Liaqunov's Method; Fixed Point Theorems; 常微分方程式系; 安定性; 漸近的性質; 周期解; 境界値問題; 解の振動性; リヤプノフの方法; 不動点定理; 常微分方程式; 解の一意性; 漸近性; 振動

Stability therorems obtained in articles by Murakami-Yamamoto [3] [13], Wada-Yamamoto [4] [11], Saito-Yamamoto [6] [10], and Ohe-yamamoto [7] [15] are extensitions of many results.Oscillation theorems for second order nonlinear differential equations by Nagabuchi-Yamamoto [2] are extensions of those obtained by yan in 1986.On the existence of periodic solutions of nonlinear systems are considered in Saito-Yamamoto [5] and Sugie-Yamamoto [14] and had new results.Uniqueness theorems of periodic solutions of Lineard equations are proved in Hirano-Yamamoto [1] [12].Existence theorems of solutions for quasilinear systems are proved in Saito-Yamamoto [8] [9].Continuous dependence of periodic solutions for periodic systems are discussed in Saito-Yamamoto [16] and obtained extensions of the theorems due to Cronin, Hale and Mawhin respectively.All results above are extensions of those obtained by many authors. Throughout the above articles, it can be considered that almost all of our purpose had been achieved.

Murakami-Yamamoto [3] [13]、Wada-Yamamoto [4] [11]、Saito-Yamamoto [6] [10] 和 Ohe-yamamoto [7] [15] 文章中获得的稳定性定理是许多结果的扩展。 Nagabuchi-Yamamoto [2] 的二阶非线性微分方程的振荡定理是这些定理的扩展 yan 于 1986 年获得。 Saito-Yamamoto [5] 和 Sugie-Yamamoto [14] 考虑了非线性系统周期解的存在性，并得到了新的结果。 Hirano-Yamamoto [1] [12] 证明了 Lineard 方程周期解的唯一性定理。 拟线性系统解的存在性定理在 Saito-Yamamoto [8] [9]。Saito-Yamamoto [16] 讨论了周期系统周期解的连续相关性，并分别得到了 Cronin、Hale 和 Mawhin 定理的扩展。以上所有结果都是许多作者获得的结果的扩展。通过上面的文章，可以认为我们的目的几乎已经达到了。

项目成果

Hirano,Masaki;Yamamoto,Minoru: "The Uniqueness of Periodic Solutions of Lienard Equations in Some Domains Including the Origin" Proceedoigs of Japan Acadey. 64. 231-234 (1988)

平野正树；山本稔：《李纳德方程周期解在某些领域的唯一性，包括起源》日本学园论文集。

Saito,Seiji;Yamamoto,Minoru: "Periodic Solutions for the Periodic Quasilinear Ordinary Differential System" Mathematical Japonica. 34. 111-121 (1989)

Saito，Seiji；Yamamoto，Minoru：“周期拟线性常微分系统的周期解”Mathematica Japonica。

Wada,Teruyo;Yamamoto,Minoru: "Asymptotic Stability Theorems for a Nonlinear Second Order Differenrial Equation" Mathematical Japonica. 34. 319-331 (1989)

Wada，Teruyo；Yamamoto，Minoru：“非线性二阶微分方程的渐近稳定性定理”数学日本。

Maruo,Kenji: "On the Existence of Solutions for Hyperbolic Equation with Subdifferential Operators Depending on Times" to appear.

Maruo、Kenji：“论含次微分算子的双曲方程解的存在性”出现。

Hirano, Masaki & Yamamoto, Minoru: "The Uniqueness of Periodic Solutions of Lienard Equations in Some Domains Including the Origin" Math. Japon.Vol. 34, No. 5. 737-746 (1989)

平野正树