<p>This paper studies the approximate controllability of a class of abstract semilinear control systems in Hilbert spaces with delay in state and control both variables via the semigroup theory. The fundamental solution is defined for delay systems. The nonlinear map is assumed to satisfy the local Lipschitz condition and a growth condition. While relaxing the compactness condition in the analysis, the concepts of degree theory, Kuratowski measure of noncompactness and condensing maps have been analyzed to establish the controllability result. Two examples have been worked out to explicate the applications of obtained theoretical results.</p>

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Degree theory analysis of semilinear control systems with delay in state and control

  • Kamlesh Raghuwanshi,
  • Suman Kumar

摘要

This paper studies the approximate controllability of a class of abstract semilinear control systems in Hilbert spaces with delay in state and control both variables via the semigroup theory. The fundamental solution is defined for delay systems. The nonlinear map is assumed to satisfy the local Lipschitz condition and a growth condition. While relaxing the compactness condition in the analysis, the concepts of degree theory, Kuratowski measure of noncompactness and condensing maps have been analyzed to establish the controllability result. Two examples have been worked out to explicate the applications of obtained theoretical results.