QUALITATIVE THEOR OF SOLUTION OF DIFFERENTIAL EQUATIONS WITH DELAYS

时滞微分方程解的定性理论

• 批准号: 12640155
• 负责人: HINO Yoshiyuki
• 金额: $ 2.5万
• 依托单位: CHIBA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640155/
• 关键词: DELAY EQUATIONS; STABILITY; PERIODIC SOLUTION; ALMOST PERIODIC SOLUTION; LIMITING EQUATIONS; 定義変化法の公式; フロッケの定理; 定数変化法の公式

Let B = B((-∞, 0] ; X), where X is a complete metric space. Consider functional differential equations with infinite delay.du/dt= Au(t) + L(t, u_t),where A is an infinitesimal generator of a compact semigroup of bounded lineat operators and u_t is an element of B defined by u_t(s) = u(t + s), s ∈ (-∞, 0].This phase space has two types, that is, one is a uniform fading memory space and the other is a fading memory space. Furthermore, if we consider an evolution equations which is a generalization of partial differential equations, above equation must be considered a functional partial differential equation with infinite delay. In this report, we have the following for the above equations.(i) Equivalent relationship between ρ-stabilities and BC-stabilities are shown.(ii) BC-total stability for a limiting equation implies that of the given euqation. BC-uniform asymptotic stabilituy also has the same property, under the uniqueness of the solution for the initial value problem.(iii) BC-total stability and BC-uniform asymtotic stability implies the existence of almost periodic solution of almost periodic euquations under the assumption of the existence of a bounded solution.

设B = B（（-∞，0] ; X），其中X是完备度量空间.考虑无穷时滞泛函微分方程du/dt= Au（t）+ L（t，ut），其中A是有界线性算子紧半群的无穷小生成元，ut是B的元素，定义为ut（s）= u（t + s），s ∈（-∞，0].进一步地，如果我们考虑一个发展方程，它是偏微分方程的推广，则上述方程必须被认为是一个具有无穷时滞的泛函偏微分方程。在这份报告中，我们有以下的上述方程。(i)证明了ρ-稳定性与BC-稳定性之间的等价关系。(ii)极限方程的BC-全稳定性蕴涵着所给方程的BC-全稳定性。在初值问题解的唯一性条件下，BC-一致渐近稳定性也具有相同的性质。(iii)在概周期方程存在有界解的假设下，BC-全稳定性和BC-一致渐近稳定性意味着概周期方程的概周期解的存在性。

项目成果

日野義之, 村上悟, 内藤敏機, N.V.Minh: "A variation-of-constants formula for abstract functional differential equations in the phase space"Journal of Differential Eqations. 179. 336-355 (2002)

Yoshiyuki Hino、Satoru Murakami、Toshiki Naito、N.V.Minh：“相空间中抽象泛函微分方程的常数变分公式”微分方程杂志 179. 336-355 (2002)。

日野義之, 村上悟: "Total stability in abstract functional differential equations with infinite delay"Electronic J.of Qualitive Theory of Differential Equations. 13. 1-9 (2000)

Yoshiyuki Hino、Satoru Murakami：“具有无限延迟的抽象泛函微分方程的完全稳定性”Electronic J.of Qualitive Theory of Differential Equations 13. 1-9 (2000)。

日野義之,村上悟,内藤敏機,N.V.Minh: "a variation -of- constants formular for abstract function differential equations in the phase space"Joural of Differential Equations. (発表予定).

Yoshiyuki Hino、Satoru Murakami、Toshiki Naito、N.V. Minh：“相空间中抽象函数微分方程的常数变分公式”《微分方程杂志》（待发表）。

Yosiyuki Hino, Satoru Murakami, Toshiki Naito, Nguyen Van Minh: "A variation-of-constants formula for abstract functional differential equations in the phase space"J. Differential Equations. 179. 336-355 (2002)

Yosiyuki Hino、Satoru Murakami、Toshiki Naito、Nguyen Van Minh：“相空间中抽象泛函微分方程的常数变分公式”J。

Yosiyuki Hino, Satoru Murakami: "Quasi-processes and stabilities in functional differential equations"Nonlinear Analysis. 47. 4025-4036 (2001)

Yosiyuki Hino、Satoru Murakami：“泛函微分方程中的拟过程和稳定性”非线性分析。