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Oscillations of high order neutral differential equations with oscillatory coefficient. (English) Zbl 0743.34076

Sufficient conditions are obtained for the oscillation of all solutions of a class of \(n\)-th order neutral functional differential equations of the form \((y(t)+p(t)y(h(t)))^{(n)}+q(t)y(g(t))=0\), where \(p,q,h\) and \(g\in C([t_ 0,\infty),R)\) such that \(q(t)>0\), \(h(t)\to\infty\), \(g(t)\to\infty\) as \(t\to\infty\) and \(n\geq 2\). Here the coefficient \(p(t)\) is assumed to be oscillatory. Examples are given to illustrate the results.

MSC:

34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34K40 Neutral functional-differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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References:

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