T. Tadumadze and L. Alkhazishvili

Formulas of Variation of Solution for Non-Linear Controlled Delay Differential Equations with Discontinuous Initial Condition

abstract:
Formulas of variation of solution of a non-linear controlled differential equation with variable delays and with discontinuous initial condition are proved. The discontinuous initial condition means that at the initial moment the values of the initial function and the trajectory, generally speaking, do not coincide. The obtained ones, in contrast to the well-known formulas, contain new terms which are connected with the variation of the initial moment and discontinuity of the initial condition.

Mathematics Subject Classification: 34K99.

Key words and phrases: Delay differential equation, variation formulas of solution.