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Controllability of Second-Order Impulsive Nonlocal Cauchy Problem Via Measure of Noncompactness

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Abstract

In this article, we consider a class of second-order impulsive evolution differential equations with nonlocal conditions. This article deals with the nonlocal controllability for a class of second-order evolution impulsive control systems. We prove some sufficient conditions for controllability using the measure of noncompactness and Mönch fixed point theorem. Very particularly we do not assume that the evolution system generates a compact semigroup. Finally, an example is given to represent the obtained theory.

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Authors and Affiliations

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

    V. Vijayakumar

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

    R. Murugesu

  3. Department of Mathematics, Kongunadu Arts and Science College, Coimbatore, Tamil Nadu, 641 029, India

    R. Poongodi & S. Dhanalakshmi

Authors
  1. V. Vijayakumar
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  2. R. Murugesu
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  3. R. Poongodi
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  4. S. Dhanalakshmi
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Correspondence to V. Vijayakumar.

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Vijayakumar, V., Murugesu, R., Poongodi, R. et al. Controllability of Second-Order Impulsive Nonlocal Cauchy Problem Via Measure of Noncompactness. Mediterr. J. Math. 14, 3 (2017). https://doi.org/10.1007/s00009-016-0813-6

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  • DOI: https://doi.org/10.1007/s00009-016-0813-6

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