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The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition

Author

Listed:
  • A. Nachaoui

    (Jean Leray Laboratory of Mathematics, University of Nantes, CNRS UMR 6629 2 rue de Houssiniere, B.P. 92208, 44322 Nantes, France)

  • T. Shavadze

    (I. Vekua Institute of Applied Mathematics, 2 University St., 0186 Tbilisi, Georgia)

  • T. Tadumadze

    (I. Vekua Institute of Applied Mathematics, 2 University St., 0186 Tbilisi, Georgia
    Department of Mathematics, Iv. Javakhishvili Tbilisi State University, 0186 Tbilisi, Georgia)

Abstract

For the perturbed controlled nonlinear delay differential equation with the discontinuous initial condition, a formula of the analytic representation of solution is proved in the left neighborhood of the endpoint of the main interval. In the formula, the effects of perturbations of the delay parameter, the initial vector, the initial and control functions are detected.

Suggested Citation

  • A. Nachaoui & T. Shavadze & T. Tadumadze, 2020. "The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1845-:d:431665
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