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Oscillations in Higher-Order Neutral Differential Equations

Published online by Cambridge University Press:  20 November 2018

CH. G. Philos
Affiliation:
Department of Mathematics, University of loannina, P.O. Box 1186, 451 10 loannina, Greece
I. K. Purnaras
Affiliation:
Department of Mathematics, University of loannina, P.O. Box 1186, 451 10 loannina, Greece
Y. G. Sficas
Affiliation:
Department of Mathematics, University of loannina, P.O. Box 1186, 451 10 loannina, Greece
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Abstract

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Consider the n-th order (n ≥ 1 ) neutral differential equation where σ1 < σ 2 < ∞ and μ and η are increasing real-valued functions on [Ƭ1, Ƭ2] and [σ1, σ2] respectively. The function μ is assumed to be not constant on [Ƭ1, Ƭ2] and [Ƭ1, Ƭ2] for every Ƭ ∈ (Ƭ1, Ƭ2) similarly, for each σ ∈ (σ1, σ2), it is supposed that r\ is not constant on [σ1 , σ] and [σ, σ2]. Under some mild restrictions on Ƭ1,- and σ1, (ι = 1,2), it is proved that all solutions of (E) are oscillatory if and only if the characteristic equation of (E) has no real roots.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1993

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