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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Oscillations in neutral equations with periodic coefficients

Authors: G. Ladas, Ch. G. Philos and Y. G. Sficas
Journal: Proc. Amer. Math. Soc. 113 (1991), 123-134
MSC: Primary 34K15; Secondary 34C10
MathSciNet review: 1045596
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Abstract: We obtain a necessary and sufficient condition for the oscillation of all solutions of the neutral delay differential equation: (1)

$\displaystyle \tfrac{d}{{dt}}[x(t) + px(t - \tau )] + Q(t)x(t - \sigma ) = 0,$

where $ p \in {\mathbf{R}},Q \in C[[0,\infty ),{{\mathbf{R}}^ + }],Q$ is $ \omega $-periodic with $ \omega > 0,Q(t)[unk]0$ for $ t \geqq 0$, and there exist positive integers $ {n_1}$ and $ {n_2}$ such that $ \tau = {n_1}\omega $ and $ \sigma = {n_2}\omega $. More precisely we show that every solution of (1) oscillates if and only if every solution of an associated neutral equation with constant coefficients oscillates.

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Article copyright: © Copyright 1991 American Mathematical Society