MMN-4795
On the representation of solution for a class of perturbed controlled neutral functional-differential equation with the continuous initial condition
Ia Ramishvili; Tea Shavadze; Tamaz Tadumazde;Abstract
The analytic relation between of solutions of the original Cauchy problem and a corresponding perturbed problem is established for the controlled neutral functional-differential equation with the continuous initial condition, whose right-hand side is linear with respect to the prehistory of the phase velocity. In the representation formula of solution the effects of perturbations of the delay parameter containing in the phase coordinates, of the initial and control functions are revealed. Continuity at the initial moment means that at the initial moment values
of the initial function and trajectory always coincide. The representation formula of solution plays an important role in proving the necessary conditions of optimality in neutral optimization
problems, allows one to get an approximate solution of the perturbed equation and to carry out a sensitivity analysis of mathematical models.
Vol. 27 (2026), No. 1, pp. 315-327