• Title/Summary/Keyword: lipschtiz continuity

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CONTROLLABILITY FOR TRAJECTORIES OF SEMILINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS

  • Jeong, Jin-Mun;Kang, Yong Han
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.63-79
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    • 2018
  • In this paper, we first consider the existence and regularity of solutions of the semilinear control system under natural assumptions such as the local Lipschtiz continuity of nonlinear term. Thereafter, we will also establish the approximate controllability for the equation when the corresponding linear system is approximately controllable.

EXISTENCE AND REGULARITY FOR SEMILINEAR NEUTRAL DIFFERENTIAL EQUATIONS IN HILBERT SPACES

  • Jeong, Jin-Mun
    • East Asian mathematical journal
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    • v.30 no.5
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    • pp.631-637
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    • 2014
  • In this paper, we construct some results on the existence and regularity for solutions of neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the existence and regularity for solutions of the neutral system by using fractional power of operators and the local Lipschtiz continuity of nonlinear term without using many of the strong restrictions considering in the previous literature.

APPROXIMATE REACHABLE SETS FOR RETARDED SEMILINEAR CONTROL SYSTEMS

  • KIM, DAEWOOK;JEONG, JIN-MUN
    • Journal of applied mathematics & informatics
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    • v.38 no.5_6
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    • pp.469-481
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    • 2020
  • In this paper, we consider a control system for semilinear differential equations in Hilbert spaces with Lipschitz continuous nonlinear term. Our method is to find the equivalence of approximate controllability for the given semilinear system and the linear system excluded the nonlinear term, which is based on results on regularity for the mild solution and estimates of the fundamental solution.