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On oscillation of solutions of second-order systems of deviated differential equations. (English) Zbl 0868.34054

Summary: Sufficient conditions are found for the oscillation of proper solutions of the system of differential equations \[ \begin{aligned} u_1'(t)=f_1(t,u_1(\tau_1(t)), \dots,u_1(\tau_m(t)),u_2(\sigma_1(t)),\dots,u_2(\sigma_m(t))),\\ u_2'(t)=f_2(t,u_1(\tau_1(t)),\dots,u_1(\tau_m(t)),u_2(\sigma_1(t)), \dots,u_2(\sigma_m(t))),\end{aligned} \] where \(f_i:\mathbb{R}_+\times \mathbb{R}^{2m}\to \mathbb{R}\) \((i=1,2)\) satisfy the local Carathéodory conditions and \(\sigma_i,\tau_i: \mathbb{R}_+\to \mathbb{R}\) \((i=1,\dots,m)\) are continuous functions such that \(\sigma_i(t)\leq t\) for \(t\in \mathbb{R}_+\), \(\lim_{t\to+\infty}\sigma_i(t)=+\infty\), \(\lim_{t\to+\infty}\tau_i(t)=+\infty\) (\(i=1,\dots,m\)).

MSC:

34K11 Oscillation theory of functional-differential equations
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References:

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