On oscilation and asymptotic behaviour of solutions of one system of differential-functional equations of neutral type
Keywords:
-Abstract
Conditions for the oscillation of all solutions and for the existence of nonoscillatory solutions with polynomial growth at infinity are given for the system of differential-functional equations of neutral type
\(\frac{{d^n }}{{dt^n }}[x(t) + \lambda _1 x(t - \tau _1 )] = p(t)f(y(\theta _1 (f)), \\ \frac{{d^n }}{{dt^n }}[y(t) + \lambda _2 y(t - \tau _2 )]q = (t)g(x(\theta _2 (t)), \\ 0 \leqslant |\lambda _1 |,|\lambda _2 |< 1. \)
References
Иванов А. Ф., Кусано Т. Колеблемость решений одного класса функционально-дифференциальных уравнений первого порядка нейтрального типа // Укр. мат. журн.— 1989.— 41, № 10.—С. 1370—1375.
Marusiak Р. Oscillation of solutions of nonlinear delay differential equations // Mat. Cas.— 1974.— N 4.— P. 371—380.
Kuan J. Types and criteria of nonoscillatory solutions for second order linear neutral differential diiference equations//Chin. Ann. Math. Ser, A.— 1987.— 8.— P. 114—124.
