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**On delay-independent criteria for oscillation of higher-order functional differential equations.**
*(English)*
Zbl 1222.34081

Summary: We investigate the oscillation of the following higher-order functional differential equation:

\[ x^{(n)}(t) + q(t)|x(t - \tau)|^{\lambda - 1}x(t - \tau) = e(t), \]

where \(q\) and \(e\) are continuous functions on \([t_0, \infty)\), \(1 > \lambda > 0\) and \(\tau \neq 0\) are constants. Unlike most of the delay-dependent oscillation results in the literature, two delay-independent oscillation criteria for the equation are established in both the case \(\tau > 0\) and the case \(\tau < 0\) under the assumption that the potentials \(q\) and \(e\) change signs on \([t_0, \infty)\).

\[ x^{(n)}(t) + q(t)|x(t - \tau)|^{\lambda - 1}x(t - \tau) = e(t), \]

where \(q\) and \(e\) are continuous functions on \([t_0, \infty)\), \(1 > \lambda > 0\) and \(\tau \neq 0\) are constants. Unlike most of the delay-dependent oscillation results in the literature, two delay-independent oscillation criteria for the equation are established in both the case \(\tau > 0\) and the case \(\tau < 0\) under the assumption that the potentials \(q\) and \(e\) change signs on \([t_0, \infty)\).

### MSC:

34K11 | Oscillation theory of functional-differential equations |

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\textit{Y. Sun}, Abstr. Appl. Anal. 2011, Article ID 173158, 6 p. (2011; Zbl 1222.34081)

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### References:

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