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Oscillations of higher order neutral differential equations of mixed type. (English) Zbl 0949.34056

Oscillatory properties of the solutions to the neutral higher-order functional-differential equation of mixed type

$\frac{{d}^{n}}{d{t}^{n}}\left(x\left(t\right)+cx\left(t-h\right)+Cx\left(t+H\right)\right)+qx\left(t-g\right)+Qx\left(t+G\right)=0$

are considered. Here, $c$, $C$, $g$, $G$, $h$ and $H$ are real constants, and $q$ and $Q$ are nonnegative real constants. Theorems are proved that give sufficient conditions for all solutions to be oscillatory. They improve results by S. R. Grace [Appl. Math. Comput. 68, No. 1, 1-13 (1995; Zbl 0829.34058)]. The proof is based on the study of the corresponding characteristic equation.

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