On asymptotic behaviour of solutions of functional differential equations

Koplatadze, Roman

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In the paper we study the existence of nonoscillatory solutions of the system $x_{i}^{(n)} (t) = \sum_{j = 1}^{2} p_{i j} (t) f_{i j} (x_{j} (h_{i j} (t))), n \geq 2, i = 1, 2$ , with the property $l i m_{t \to \infty} x_{i} (t) / t^{k_{i}} = c o n s t \neq 0$ for some $k_{i} \in {1, 2, ..., n - 1}, i = 1, 2$ . Sufficient conditions for the oscillation of solutions of the system are also proved.