Continuity of Solution with Respect to Initial Data for One Class of Controlled Functional Differential Equation with Distributed Delay Uniformly with Control Function

Author: Giorgi Adeishvili
Keywords: functional differential equation, distributed delay
Annotation:

For the controlled nonlinear differential equation with distributed delay in the phase coordinates is proved theorem about continuous dependence of solution on initial data uniformly with respect to control functions. Under the initial data we mean the collection of the initial moment, delay parameter, initial function and initial vector. Perturbations of the initial data are small in a standard norm. Moreover, sensitivity of the existence of a solution (optimal control) for an optimal problem is investigated with respect to perturbations of initial data. Namely, is proved that if the initial optimal problem has a solution then perturbed problem has solution also.

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ამონახსნის უწყვეტობა საწყისი მონაცემების მიმართ ერთი კლასის სამართი ფუნქციონალურ-დიფერენციალური განტოლებისათვის განაწილებული დაგვიანებით თანაბრად მართვის ფუნქციების მიმართ [ka]