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Theorems on the continuous dependence of a solution of the Cauchy problem with respect to the nonlinear term of the right-hand side and initial data are proved for neutral functional differential equations whose right-hand sides are linear with respect to the prehistory of the phase velocity. Under the initial data we imply a collection of initial moment, variable delays entering in the phase coordinates, initial vector and initial functions. In this paper, an essential novelty is that perturbations of variable delays are taken into account in proving the main theorems.

georgian mathematical journal

Continuous dependence of a solution of a neutral functional differential equation on the right-hand side and initial data taking into account perturbations of variable delays