Controllability of nonlocal impulsive functional differential equations with measure of noncompactness in Banach spaces

Volume 14, Issue 6, pp 400--413 http://dx.doi.org/10.22436/jnsa.014.06.03

Publication Date: May 09, 2021 Submission Date: October 16, 2020 Revision Date: November 23, 2020 Accteptance Date: March 18, 2021

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Authors

D. N. Chalishajar - Department of Applied Mathematics, Virginia Military Institute (VMI), 435, Mallory Hall, Lexington, VA 24450, USA. K. Karthikeyan - Department of Mathematics \(\&\) Centre for Research and Development, KPR Institute of Engineering and Technology, Coimbatore- 641 407, Tamil Nadu, India. D. Tamizharasan - Department of Mathematics, KSR College of Technology, Tiruchengode 637 215, Tamilnadu, India.

Abstract

This paper is concerned with the controllability of impulsive differential equations with nonlocal conditions. First, we establish a property of measure of noncompactness in the space of piecewise continuous functions. Then, by using this property and Darbo-Sadovskii's fixed point theorem, we get the controllability of nonlocal impulsive differential equations under compactness conditions, Lipschitz conditions, and mixed-type conditions, respectively.

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Keywords

• Controllability
• impulsive differential equations
• nonlocal conditions
• measure of non compactness
• fixed point theorem

MSC

•  34K30
•  34K35
•  35R10
•  60G99
•  93C10

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