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On oscillation of solutions of forced nonlinear neutral differential equations of higher order II. (English) Zbl 1037.34058

The authors consider \(n\)th-order forced nonlinear neutral differential equations of the form \[ [y(t)-p(t)y(t-\tau)]^{(n)}+Q(t)G(y(t-\sigma))=f(t), \tag{1} \] with \(n\geq 2\), \(p,f\in C([0,\infty),\mathbb R)\), \(Q\in C([0,\infty),[0,\infty))\), \(G\in C(\mathbb R,\mathbb R)\), \(\tau>0\) and \(\sigma\geq 0\). They give conditions which guarantee that every solution to equation (1) oscillates or tends to zero as \(t\to\infty\). In most of the results, it is assumed that \(\int_{0}^{\infty}Q(t)\,dt=\infty\).
For part I see Proc. Indian Acad. Sci., Math. Sci. 111, 337–350 (2001; Zbl 0995.34058).

MSC:

34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations

Citations:

Zbl 0995.34058
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