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Oscillatory properties of nonlinear differential systems with retarded arguments. (English) Zbl 1115.34063
The authors consider the nonlinear differential system \[ \begin{aligned} y'_i(t) - p_i(t)y_{i+1}(t)&=0,\qquad i=1,2,\dots , n-2, \\ y'_{n-1}(t) - p_{n-1}(x)| y_n\bigl (h_n(t)\bigr )| ^{\alpha } \text{sgn}\bigl [y_n\bigl (h_n(t)\bigr )\bigr ]&=0, \\ y'_n(t) \text{sgn}\bigl [y_1\bigl (h_1(t)\bigr )\bigr ]+ p_n(t)\bigl | y_1\bigl (h_1(t)\bigr )\bigr | ^{\beta }& \leq 0. \end{aligned} \tag{1} \]
Under some assumptions on the functions \(p_i\), \(i=1,\dots , n\), and \(h_1, h_n\) they establish sufficient conditions for the oscillatory properties of (1). The problem of oscillation of all solutions is treated.

MSC:
34K11 Oscillation theory of functional-differential equations
Keywords:
oscillatory
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References:
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