Research Article

A study on approximate controllability of linear impulsive equations in Hilbert spaces

Published in: Quaestiones Mathematicae
Volume 47 , issue 9 , 2024 , pages: 1791–1806

DOI: 10.2989/16073606.2024.2345287

Author(s): Nazim I. Mahmudov Eastern Mediterranean University, Turkey

Keywords: 93B05 , 34K30 , 34K45 , 34A12 , Approximate controllability , existence and uniqueness , impulsive systems

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Abstract

In this paper, we study an approximate controllability for the impulsive linear evolution equations in Hilbert spaces. We give a representation of solution in terms of semigroup and impulsive operators. We present the necessary and sufficient conditions for approximate controllability of linear impulsive evolution equation in terms of impulsive resolvent operator. An example is provided to illustrate the application of the obtained results.

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