Existence and Approximate Controllability Results for the Second-Order Abstract Neutral Differential System with Damping

IF 1.9 3区数学 Q1 MATHEMATICS

Qualitative Theory of Dynamical Systems Pub Date : 2023-11-22 DOI:10.1007/s12346-023-00898-6

W. Kavitha Williams, V. Vijayakumar

引用次数: 0

Abstract

In this paper, we investigate the approximate controllability of mild solutions for second-order differential systems. Using principles and ideas from the theory of the cosine family of operators and the fixed-point approach, we verify the existence of mild solutions for the given system. A new set of sufficient conditions is formulated and proved for the approximate controllability of second-order differential systems under the assumption that the associated linear part of the system is approximately controllable. In addition, we extend our system with nonlocal conditions. Our research on approximate controllability was also extended by utilizing impulse systems. To demonstrate the theory of the primary outcomes, an application is shown.

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二阶带阻尼抽象中立型微分系统的存在性及近似可控性结果

本文研究二阶微分系统温和解的近似可控性。利用余弦算子族理论和不动点方法的原理和思想，验证了给定系统温和解的存在性。在二阶微分系统相关线性部分近似可控的前提下，构造并证明了二阶微分系统近似可控的一组新的充分条件。此外，我们用非局部条件扩展了我们的系统。利用脉冲系统扩展了近似可控性的研究。为了证明主要结果的理论，给出了一个应用。

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

Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

14.30%

发文量

130

期刊介绍： Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.