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Formulas of variation of solution for nonlinear controlled delay differential equations with discontinuous initial condition. (English) Zbl 1065.49019

Summary: Formulas of solution variations 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 formulas, in contrast to their continuous counterparts, contain new terms which are connected with the variation of the initial moment and discontinuity of the initial condition.

MSC:

49K25 Optimal control problems with equations with ret.arguments (nec.) (MSC2000)
34K35 Control problems for functional-differential equations
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