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

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.