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Mild Solution and Approximate Controllability of Second-Order Retarded Systems with Control Delays and Nonlocal Conditions

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Abstract

This work studies the approximate controllability of a class of second-order retarded semilinear differential equations with nonlocal conditions and with delays in control. First, we deduce the existence of mild solutions using cosine family and fixed point approach. For this, the nonlinear function is supposed to be locally Lipschitz. Controllability of the system is shown using an approximate and iterative technique. The results are illustrated using an example.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247667, India

    Abdul Haq & N. Sukavanam

Authors
  1. Abdul Haq
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  2. N. Sukavanam
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Correspondence to Abdul Haq.

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Communicated by Majid Gazor.

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Haq, A., Sukavanam, N. Mild Solution and Approximate Controllability of Second-Order Retarded Systems with Control Delays and Nonlocal Conditions. Bull. Iran. Math. Soc. 48, 447–464 (2022). https://doi.org/10.1007/s41980-021-00527-5

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  • DOI: https://doi.org/10.1007/s41980-021-00527-5

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