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Oscillations of higher order neutral differential equations

Part of: Functional-differential and differential-difference equations Qualitative theory

Published online by Cambridge University Press:  09 April 2009

S. J. Bilchev ,
M. K. Grammatikopoulos  and
I. P. Stavroulakis
S. J. Bilchev
Affiliation:
Technical University7017 Rousse, Bulgaria
M. K. Grammatikopoulos
Affiliation:
University of Ioannina451 10 Ioannina, Greece
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Abstract

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Consider the nth-order neutral differential equation where n ≥ 1, δ = ±1, I, K are initial segments of natural numbers, pi, τi, σk ∈ R and qk ≥ 0 for i ∈ I and k ∈ K. Then a necessary and sufficient condition for the oscillation of all solutions of (E) is that its characteristic equation has no real roots. The method of proof has the advantage that it results in easily verifiable sufficient conditions (in terms of the coefficients and the arguments only) for the oscillation of all solutionso of Equation (E).

MSC classification

Secondary: 34K40: Neutral equations 34C10: Oscillation theory, zeros, disconjugacy and comparison theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 52 , Issue 2 , April 1992 , pp. 261 - 284
Copyright
Copyright © Australian Mathematical Society 1992

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