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Approximate Controllability of Second-Order Evolution Differential Inclusions in Hilbert Spaces

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Abstract

In this paper, we consider a class of second-order evolution differential inclusions in Hilbert spaces. This paper deals with the approximate controllability for a class of second-order control systems. First, we establish a set of sufficient conditions for the approximate controllability for a class of second-order evolution differential inclusions in Hilbert spaces. We use Bohnenblust–Karlin’s fixed point theorem to prove our main results. Further, we extend the result to study the approximate controllability concept with nonlocal conditions and also extend the result to study the approximate controllability for impulsive control systems with nonlocal conditions. An example is also given to illustrate our main results.

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Authors and Affiliations

  1. Department of Mathematics, Eastern Mediterranean University, Gazimagusa, T. R. North Cyprus, Mersin 10, Turkey

    N. I. Mahmudov

  2. Department of Mathematics, Info Institute of Engineering, Kovilpalayam, Coimbatore, 641 107, Tamil Nadu, India

    V. Vijayakumar

  3. Department of Mathematics, SRMV College of Arts and Science, Coimbatore, 641 020, Tamil Nadu, India

    R. Murugesu

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  1. N. I. Mahmudov
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  2. V. Vijayakumar
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  3. R. Murugesu
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Mahmudov, N.I., Vijayakumar, V. & Murugesu, R. Approximate Controllability of Second-Order Evolution Differential Inclusions in Hilbert Spaces. Mediterr. J. Math. 13, 3433–3454 (2016). https://doi.org/10.1007/s00009-016-0695-7

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