On the existence of solution of the two-stage optimal problem containing a delay factor

The existence theorem is proved for the nonlinear two-stage optimal problem with the constant delay parameters in the phase coordinates, with the discontinuous intermediate condition and the phase restrictions, with the general boundary condition and functional. Under solution we imply the collection of delay parameters and moment of change stage of system and controls. The result obtained here is concretized for the quasi-linear and linear problems, for the problems, for the optimal problem with the integral functional also.

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