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Controllability results for semilinear impulsive integrodifferential evolution systems with nonlocal conditions

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Abstract

In this paper, we establish sufficient conditions for the controllability of a class of semilinear impulsive integrodifferential systems with nonlocal initial conditions in Banach spaces. We derive the conditions using Hausdorff measure of noncompactness, Sadovskii fixed point theorem and operator semigroups in particular dropping compactness of the operator.

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Authors and Affiliations

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

    Bheeman Radhakrishnan & Krishnan Balachandran

Authors
  1. Bheeman Radhakrishnan
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  2. Krishnan Balachandran
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Corresponding author

Correspondence to Bheeman Radhakrishnan.

Additional information

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

Bheeman RADHAKRISHNAN received his M.S. and M.Phil. degrees in Mathematics at Bharathiar University, Coimbatore, India in 2007 and 2009, respectively, and is currently pursuing the Ph.D. degree at Bharathiar University, Coimbatore, India. His current research interests are in the fields of control theory and abstract differential equation.

Krishnan BALACHANDRAN received his M.S. degree in Mathematics in 1978, 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 the editorial board of the journal Nonlinear Analysis: Hybrid Systems. He is also a member of AMS, IMS, CMS and ISCA. He was awarded the Fulbright Visiting Fellowship at the University of Tennessee at Chattanooga, USA, in 1996. He is 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 University Wyoming, USA (2004). He was Visiting Professor at Sophia University, Tokyo, Japan (1998) and 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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Radhakrishnan, B., Balachandran, K. Controllability results for semilinear impulsive integrodifferential evolution systems with nonlocal conditions. J. Control Theory Appl. 10, 28–34 (2012). https://doi.org/10.1007/s11768-012-0188-6

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  • DOI: https://doi.org/10.1007/s11768-012-0188-6

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