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Zbl 0997.34059
Ou, C.H.; Wong, James S.W.
Forced oscillation of $n$th-order functional differential equations.
(English)
[J] J. Math. Anal. Appl. 262, No.2, 722-732 (2001). ISSN 0022-247X

Here, the authors consider the oscillation of forced functional-differential equations $$x^{(n)}(t)+a(t)f(x(q(t)))=e(t),\tag 1$$ when the forcing term is not required to be the $n$th derivative of an oscillatory function. Several new oscillation criteria and explicit oscillation results are given. For example, if $a(t)\geq 0$, $\beta>0$ and $$\lim_{t\rightarrow\infty}\inf \frac{1}{(t-t_0)^{\beta}} \int_{t_0}^t (t-s)^{\beta}e(s) ds =-\infty,\ \lim_{t\rightarrow\infty}\sup \frac{1}{(t-t_0)^{\beta}} \int_{t_0}^t (t-s)^{\beta}e(s) ds =+\infty,$$ then equation (1) is oscillatory. Forced neutral differential equations are also considered.
[Leonid Berezanski (Beer-Sheva)]
MSC 2000:
*34K11 Oscillation theory of functional-differential equations
34K40 Neutral equations

Keywords: oscillation; forced term; delay; neutral equation

Cited in: Zbl 1158.34026 Zbl 1064.34020

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