On oscilation and asymptotic behaviour of solutions of one system of differential-functional equations of neutral type

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

$\frac{{d^n }}{{dt^n }}[x(t) + \lambda _1 x(t - \tau _1 )] = p(t)f(y(\theta _1 (f)), \\ \frac{{d^n }}{{dt^n }}[y(t) + \lambda _2 y(t - \tau _2 )]q = (t)g(x(\theta _2 (t)),  \\ 0 \leqslant |\lambda _1 |,|\lambda _2 |< 1.$