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Oscillations in Higher-Order Neutral Differential Equations

Published online by Cambridge University Press:  20 November 2018

CH. G. Philos ,
I. K. Purnaras  and
Y. G. Sficas
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 [Ƭ 1, Ƭ 2] and [σ1, σ2] respectively. The function μ is assumed to be not constant on [Ƭ 1, Ƭ 2] and [Ƭ 1, Ƭ 2] for every Ƭ ∈ (Ƭ 1, Ƭ 2) 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 Ƭ 1,- 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.

Keywords

34K15oscillationneutral differential equation

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 1 , 01 February 1993 , pp. 132 - 158
Copyright
Copyright © Canadian Mathematical Society 1993

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