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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

d n dt n (x(t)+cx(t-h)+Cx(t+H))+qx(t-g)+Qx(t+G)=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:
34K11Oscillation theory of functional-differential equations
34K40Neutral functional-differential equations
References:
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