论具有延迟论证的抽象微分方程的指数二分法

IF 0.5 4区数学 Q3 MATHEMATICS

Ukrainian Mathematical Journal Pub Date : 2023-12-08 DOI:10.1007/s11253-023-02263-x

Andrii Chaikovs’kyi, Oksana Lagoda

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引用次数: 0

摘要

我们考虑的是巴拿赫空间中具有延迟参数的一阶线性微分方程。我们建立了在实轴上存在指数二分法所需的算子系数条件。我们证明了所分析的微分方程等价于某个空间中的差分方程。结果表明，在整个实轴上有界的解的存在性和唯一性条件下，对于任何已知的有界函数，指数二分法的条件也是满足的。我们还推导出了投影器的明确公式，它在单延迟情况下形成了这种二分法。

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On Exponential Dichotomy for Abstract Differential Equations with Delayed Argument

We consider linear differential equations of the first order with delayed arguments in a Banach space. We establish conditions for the operator coefficients necessary for the existence of exponential dichotomy on the real axis. It is proved that the analyzed differential equation is equivalent to a difference equation in a certain space. It is shown that, under the conditions of existence and uniqueness of a solution bounded on the entire real axis, the condition of exponential dichotomy is also satisfied for any known bounded function. We also deduce the explicit formula for projectors, which form this dichotomy in the case of a single delay.

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来源期刊

Ukrainian Mathematical Journal MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

20.00%

发文量

107

审稿时长

4-8 weeks

期刊介绍： Ukrainian Mathematical Journal publishes articles and brief communications on various areas of pure and applied mathematics and contains sections devoted to scientific information, bibliography, and reviews of current problems. It features contributions from researchers from the Ukrainian Mathematics Institute, the major scientific centers of the Ukraine and other countries. Ukrainian Mathematical Journal is a translation of the peer-reviewed journal Ukrains’kyi Matematychnyi Zhurnal, a publication of the Institute of Mathematics of the National Academy of Sciences of Ukraine.