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functional differential system; Schauder-Tichonov fixed point theorem; oscillatory and nonoscillatory solutions; prescribed asymptotics; oscillatory solutions; nonoscillatory solutions
In the paper we study the existence of nonoscillatory solutions of the system $x^{(n)}_i(t)=\sum^2_{j=1}p_{ij}(t)f_{ij}(x_j(h_{ij}(t))), n\geq 2, i=1,2$, with the property $lim_{t\rightarrow \infty}x_i(t)/t^{k_i}=const \neq 0$ for some $k_i\in \{1,2,\ldots,n-1\}, i=1,2$. Sufficient conditions for the oscillation of solutions of the system are also proved.
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