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Controllability results for damped second-order impulsive neutral integrodifferential systems with nonlocal conditions

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Abstract

In this paper, we establish a set of sufficient conditions for the controllability of damped second-order impulsive neutral integrodifferential systems with nonlocal initial conditions in Banach spaces. The approach used is the Sadovskii fixed point theorem combined with a noncompact condition on the cosine family of operators. An example is presented to illustrate the result.

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Authors and Affiliations

  1. Department of Mathematics, Bharathiar University, Coimbatore, 641046, India

    Ganesan Arthi & Krishnan Balachandran

Authors
  1. Ganesan Arthi
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  2. Krishnan Balachandran
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Corresponding author

Correspondence to Ganesan Arthi.

Additional information

This work of Dr. Arthi was supported by University Grant Commission (UGC), India (No. G2/1287/UGC SAP DRS/2009).

Ganesan ARTHI received her M.S. and M.Phil. degrees in Mathematics at Bharathiar University, Coimbatore, India, in 2007 and 2009, respectively, and she is currently pursuing the Ph.D. degree at Bharathiar University, Coimbatore, India. Her current research interests include control theory and differential equation.

Krishnan BALACHANDRAN received his M.S. degree in Mathematics in 1978, the M.Phil. and Ph.D. degrees in Applied Mathematics, in 1980 and 1985, respectively from the University of Madras. Currently, he is working as Professor of Mathematics at Bharathiar University, Coimbatore, India. To his credit, he has published more than 250 research papers in Control Theory, Abstract Differential Equations and General Topology. He is acting as referee for various international journals. He is a member of AMS, IMS, CMS and ISCA. He was awarded the Fulbright Visiting Fellowship at the University of Tennessee at Chattanooga, U.S.A. in 1996. He was a recipient of Chandna Mathematics Award in recognition of distinguished and outstanding contributions to mathematics research and teaching in 1999. He got the Tamil Nadu Scientist Award in 2001. He was a visiting scientist at the International Centre for Theoretical Physics, Trieste, Italy (1987, 1990) and UniversityWyoming, U.S.A. (2004). He was a visiting professor at Sophia University, Tokyo, Japan (1998) and a visiting research professor at Yonsei University in 2005 and the Pusan National University, Pusan, Korea in 1999–2000 and 2008–2009.

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Arthi, G., Balachandran, K. Controllability results for damped second-order impulsive neutral integrodifferential systems with nonlocal conditions. J. Control Theory Appl. 11, 186–192 (2013). https://doi.org/10.1007/s11768-013-1084-4

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  • DOI: https://doi.org/10.1007/s11768-013-1084-4

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