Existence, uniqueness, variation-of-constant formula and controllability for linear dynamic equations with Perron Δ-integrals

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-11-30 DOI:10.1142/s1664360721500119

F. A. da Silva, M. Federson, E. Toon

引用次数: 1

Abstract

In this paper, we investigate the existence and uniqueness of a solution for a linear Volterra-Stieltjes integral equation of the second kind, as well as for a homogeneous and a nonhomogeneous linear dynamic equations on time scales, whose integral forms contain Perron [Formula: see text]-integrals defined in Banach spaces. We also provide a variation-of-constant formula for a nonhomogeneous linear dynamic equations on time scales and we establish results on controllability for linear dynamic equations. Since we work in the framework of Perron [Formula: see text]-integrals, we can handle functions not only having many discontinuities, but also being highly oscillating. Our results require weaker conditions than those in the literature. We include some examples to illustrate our main results.

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含Perron的线性动力方程的存在唯一性、常变公式和可控性Δ-integrals

本文研究了一类线性第二类Volterra-Stieltjes积分方程，以及一类齐次和非齐次线性动力方程在时间尺度上的解的存在唯一性，这些方程的积分形式包含在Banach空间中定义的Perron[公式:见文]-积分。我们还提供了时间尺度上非齐次线性动力方程的常变公式，并建立了线性动力方程的可控性结果。由于我们在Perron积分的框架下工作，我们不仅可以处理有许多不连续的函数，而且可以处理高度振荡的函数。我们的结果需要比文献中更弱的条件。我们包括一些例子来说明我们的主要结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.