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Oscillation of first-order differential equations with several non-monotone retarded arguments. (English) Zbl 1455.34068

Let \(p_i, \tau_i\in C([t_0,\infty], \mathbb{R}_+)\), \(\tau_i(t)\leq t\) and \(\lim_{t\to+\infty}\tau_i(t)=\infty\) (\(i=1,\ldots,m\)). Consider ordinary differential equation with delay of the form \[ x'(t)+\sum_{i=1}^m p_i(t)x(\tau_i(t))=0\text{ for }t\geq t_0. \] Assume that there exist non-decreasing functions \(\sigma_i\in C([t_0,\infty], \mathbb{R}_+)\) s.t. \(\tau_i(t)\leq\sigma_i(t)\leq t\) (\(i=1,\ldots,m\)). Additional conditions on the functions \(p_i\) provided such that all solutions of the differential equation oscillate. Some examples are given.

MSC:

34K11 Oscillation theory of functional-differential equations
34K06 Linear functional-differential equations
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