О построении асимптотических решений системы нелинейных дифферен- циальных уравнений с малым параметром при производных с переменным отклонением аргумента - Алишев, А.Г; Алишев, Ш.А (SCIENCE and SOCIETY, 2022)
For a system of non-linear differential equations with slowly varying coefficients, a small parameter at the highest derivatives with a variable retarded argument of a neutral addition, asymptotic solutions are constructed in the form of expansions in a series in powers of a small parameter. Studied in detail when the characteristic equation of the considered equation has a simple, semisimple and multiple zero root, when the multiple root corresponds to one Jardan chain of vectors. For the case of a simple and multiple zero root of the characteristic equation, theorems are given that indicate the asymptotic nature of formal particular solutions in the sense of Yu.A. Mitrapolskiy and S.F. Feshenko where is indicated and the distance between the exact and formal particular solution.
Keywords: vector; Taylor; equation; coefficient; root; asymptotics; differential; system; formal; expansion; series; slowly changing