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Baculíková, B.; Džurina, J.

Oscillation theorems for higher order neutral differential equations. (English) Zbl 1311.34163

Appl. Math. Comput. 219, No. 8, 3769-3778 (2012).
Summary: The aim of this paper is to study the asymptotic properties and oscillation of the \(n\)th order neutral differential equations \[ \left(r(t)[x(t)+p(t)x(\tau)t))]^{(n-1)}\right)'+q(t)x(\sigma(t))=0. \tag{E} \] Obtained results are based on the new comparison theorems, that permit to reduce the problem of the oscillation of the \(n\)th order equation to the oscillation of a set of the first order equation. Obtained comparison principles essentially simplify the examination of studied equations and allow to relax some conditions imposed on the coefficients of (E).

Cited in 23 Documents

MSC:

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

Keywords:

\(n\)th order neutral differential equations; comparison theorem; oscillation; nonoscillation
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References:

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