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

A. Nachaoui, T. Shavadze and T. Tadumadze
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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

Mathematics, 2020, vol. 8, issue 10, 1-12

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.

Keywords: delay-controlled differential equation; representation of solution; discontinuous initial condition; perturbations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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