Controllability of Nonlocal Impulsive Functional Differential Equations with Measure of Noncompactness in Banach Spaces-Reference-Cited by-同舟云学术

Controllability of Nonlocal Impulsive Functional Differential Equations with Measure of Noncompactness in Banach Spaces

Published:2021-12-01 Issue:2 Volume:79 Page:59-80
ISSN:1338-9750
Container-title:Tatra Mountains Mathematical Publications
language:en
Short-container-title:

Author:

Chalishajar Dlmplekumar N.¹,Karthikeyan Kulandhivel²,Tamizharasan Dhachinamoorthi³

Affiliation:

1. 1 Department of Applied Mathematics , Virginia Military Institute (VMI) , Mallory Hall, Lexington, VA , U.S.A

2. 2 Department of Mathematics & Centre for Research and Development , KPR Institute of Engineering and Technology , Coimbatore, TamilNadu , INDIA

3. 3 Department of Mathematics , KSR College of Technology , Tiruchengode, TamilNadu , INDIA

Abstract

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/tmmp-2021-0020

Reference34 articles.

1. [1] BYSZEWSKI, L.: Theorems about the existence and uniqueness of solutions of a semi-linear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), 494–505.10.1016/0022-247X(91)90164-U

2. [2] FITZGIBBON, W.: Semilinear interodifferential equations in Banach space, Nonlinear Anal., Theory, Methods Appl. 4 (1980), 745–760.

3. [3] LAKSHMIKANTHAM, V.—BAINOV, D. D.—SIMEONOV, P. S. D.: Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.10.1142/0906

4. [4] BENCHOHRA, M.—HENDERSON, J.—NTOUYAS, S. K.: Impulsive Differential Equations and Inclusions, Hindawi Publishing, New York, 2006.10.1155/9789775945501

5. [5] BAINOV, D. D.—SIMEONOV, P. S.: Impulsive differential equations: Periodic solutions and applications, In: Pitman Monographs and Surveys in Pure and Applied Mathematics Vol. 66. Harlow: Longman Scientific & Technical; New York, NY: John Wiley & Sons, Inc. 1993.