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Forced oscillation of \(n\)th-order functional differential equations. (English) Zbl 0997.34059

Here, the authors consider the oscillation of forced functional-differential equations \[ x^{(n)}(t)+a(t)f(x(q(t)))=e(t),\tag{1} \] when the forcing term is not required to be the \(n\)th derivative of an oscillatory function. Several new oscillation criteria and explicit oscillation results are given. For example, if \(a(t)\geq 0\), \(\beta>0\) and \[ \lim_{t\rightarrow\infty}\inf \frac{1}{(t-t_0)^{\beta}} \int_{t_0}^t (t-s)^{\beta}e(s) ds =-\infty,\;\lim_{t\rightarrow\infty}\sup \frac{1}{(t-t_0)^{\beta}} \int_{t_0}^t (t-s)^{\beta}e(s) ds =+\infty, \] then equation (1) is oscillatory. Forced neutral differential equations are also considered.

MSC:

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

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