Oscillation of neutral differential equations with periodic coefficients

Huang, Qing Guang; Chen, Shao Zhu

doi:10.1090/S0002-9939-1990-1075188-6

Oscillation of neutral differential equations with periodic coefficients
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by Qing Guang Huang and Shao Zhu Chen

Proc. Amer. Math. Soc. 110 (1990), 997-1001

DOI: https://doi.org/10.1090/S0002-9939-1990-1075188-6

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Abstract:

We establish a necessary and sufficient condition for the oscillation of all solutions to the neutral differential equation \[ [x(t) - p(x)(t - r)]’ + \sum \limits _{i = 1}^n {{q_i}(t)x(t - ir) = 0} ,\] where $0 \leq p \leq 1,r > 0$ are constants and ${q_i}(t) \geq 0,i = 1, \ldots ,n$, are continuous $r$-periodic functions.

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Necessary and sufficient conditions for the oscillation of a class of differential difference equations with sign-variable periodic coefficients

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