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On the oscillation and asymptotic behavior of the solutions of a certain system of differential-functional equations of neutral type

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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

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

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Literature cited

  1. A. F. Ivanov and T. Kusano, “Oscillations of solutions of a class of first-order functional-differential equations of neutral type,” Ukr. Mat. Zh.,41, No. 10, 1370–1375 (1974).

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  2. P. Marusiak, “Oscillations of solutions of nonlinear delay differential equations,” Mat. Cas., No. 4, 371–380 (1974).

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  3. J. Ruan, “Types and criteria of nonoscillatory solutions for second order linear neutral differential difference equations,” Chinese Ann. Math., Ser. A,8, 114–124 (1987).

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 8, pp. 1044–1049, August, 1992.

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Ivanov, A.F., Marusiak, P. On the oscillation and asymptotic behavior of the solutions of a certain system of differential-functional equations of neutral type. Ukr Math J 44, 945–949 (1992). https://doi.org/10.1007/BF01057113

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  • DOI: https://doi.org/10.1007/BF01057113

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