Opuscula Math. 35, no. 1 (2015), 71-83

Opuscula Mathematica

Controllability of semilinear systems with fixed delay in control

Surendra Kumar
N. Sukavanam

Abstract. In this paper, different sufficient conditions for exact controllability of semilinear systems with a single constant point delay in control are established in infinite dimensional space. The existence and uniqueness of mild solution is also proved under suitable assumptions. In particular, local Lipschitz continuity of a nonlinear function is used. To illustrate the developed theory some examples are given.

Keywords: first order delay system, mild solution, fixed point, exact controllability.

Mathematics Subject Classification: 93B05.

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  • Surendra Kumar
  • University of Delhi, Department of Mathematics, Delhi - 110007, India
  • N. Sukavanam
  • Indian Institute of Technology, Roorkee, Department of Mathematics, Roorkee (Uttarakhand) - 247667, India
  • Communicated by Alexander Gomilko.
  • Received: 2013-05-29.
  • Revised: 2014-02-07.
  • Accepted: 2014-03-23.
  • Published online: 2014-11-12.
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Cite this article as:
Surendra Kumar, N. Sukavanam, Controllability of semilinear systems with fixed delay in control, Opuscula Math. 35, no. 1 (2015), 71-83, http://dx.doi.org/10.7494/OpMath.2015.35.1.71

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