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Controllability of Second Order Impulsive Neutral Functional Differential Inclusions with Infinite Delay

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Abstract

This paper is concerned with controllability of a partial neutral functional differential inclusion of second order with impulse effect and infinite delay. We introduce a new phase space to prove the controllability of an inclusion which consists of an impulse effect with infinite delay. We claim that the phase space considered by different authors is not correct. We establish the controllability of mild solutions using a fixed point theorem for contraction multi-valued maps and without assuming compactness of the family of cosine operators.

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Acknowledgements

Author expresses his gratitude to the anonymous referee for valuable comments and suggestions which are helpful to improve the manuscript.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Mallory Hall, Virginia Military Institute, Lexington, VA, 24450, USA

    Dimplekumar N. Chalishajar

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  1. Dimplekumar N. Chalishajar
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Correspondence to Dimplekumar N. Chalishajar.

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Communicated by Mark J. Balas.

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Chalishajar, D.N. Controllability of Second Order Impulsive Neutral Functional Differential Inclusions with Infinite Delay. J Optim Theory Appl 154, 672–684 (2012). https://doi.org/10.1007/s10957-012-0025-6

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