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Well-posedness of the Cauchy problem for one class of neutral quasi-linear differential equation with distributed delay. (English) Zbl 1415.34125

Summary: Theorems on the continuous dependence of a solution on perturbations of the initial data and the right-hand side are given for a neutral differential equation with distributed delay in the phase coordinates and whose right-hand side is linear with respect to phase velocity. The perturbations of the initial data (initial moment, initial vector, initial functions, initial matrix, distributed delay) are small in the standard norm, the perturbation of the right-hand side of equation is small in the integral sense.

MSC:

34K40 Neutral functional-differential equations
34K27 Perturbations of functional-differential equations