Controllability of Second-Order Impulsive Nonlocal Cauchy Problem Via Measure of Noncompactness

• Published in: Mediterranean journal of mathematics Vol. 14; no. 1; pp. 1 - 23
• Main Authors: Vijayakumar, V., Murugesu, R., Poongodi, R., Dhanalakshmi, S.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01-02-2017; Springer Nature B.V
• Subjects: Controllability; Mathematics; Mathematics and Statistics; second-order abstract Cauchy problem; 47H10; 34K09; measure of noncompactness; 93B05; 26A33; 34B10; impulsive systems; Controllabiliy; nonlocal conditions
• ISSN: 1660-5446; 1660-5454
• DOI: 10.1007/s00009-016-0813-6

In this article, we consider a class of second-order impulsive evolution differential equations with nonlocal conditions. This article deals with the nonlocal controllability for a class of second-order evolution impulsive control systems. We prove some sufficient conditions for controllability using the measure of noncompactness and Mönch fixed point theorem. Very particularly we do not assume that the evolution system generates a compact semigroup. Finally, an example is given to represent the obtained theory.