Approximate Controllability of Non-autonomous Second Order Impulsive Functional Evolution Equations in Banach Spaces

被引：1

作者：

Arora, Sumit ^{[1
]}

Singh, Soniya ^{[1
]}

Mohan, Manil T. T. ^{[2
]}

Dabas, Jaydev ^{[1
]}

机构：

[1] Indian Inst Technol Roorkee, Dept Appl Math & Sci Comp, Roorkee 247667, Uttarakhand, India

[2] Indian Inst Technol Roorkee, Dept Math, Roorkee 247667, Uttarakhand, India

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2023年 / 22卷 / 01期

关键词：

Abstract functional evolution equations; Non-instantaneous impulses; Approximate controllability; Evolution operator; Cosine family; NONLINEAR DIFFERENTIAL-EQUATIONS; TIME-DEPENDENT PERTURBATION; COSINE-FAMILIES; MILD SOLUTIONS; SYSTEMS; INCLUSIONS; EXISTENCE;

D O I：

10.1007/s12346-022-00718-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article investigates the approximate controllability of second order non-autonomous functional evolution equations involving non-instantaneous impulses and nonlocal conditions. First, we discuss the approximate controllability of second order linear system in detail, which lacks in the existing literature. Then, we derive sufficient conditions for approximate controllability of our system in separable reflexive Banach spaces via linear evolution operator, resolvent operator conditions, and Schauder's fixed point theorem. Moreover, in this paper, we define proper identification of resolvent operator in Banach spaces. Finally, we provide two concrete examples to validate our results.

引用

页数：36

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