On the oscillation of functional differential equations. (English) Zbl 0935.34056
For the equation
\[
x^{(n)}(t)+p(t)x^{(n-1)}(t)+\delta H(t,x(g(t)))=0,
\]
where \(p,g:[t_0,\infty)\to{\mathbb{R}}\), \(H:[t_0,\infty)\times {\mathbb{R}}\to{\mathbb{R}}\) are continuous, \(p(t)\geq 0\), \(\lim_{t\to+\infty}g(t)=+\infty\), \(\delta=\pm 1\), some oscillations criteria are proved. The authors emphasize that conditions of the form
\[
\int_{t_0}^{\infty}\exp\Biggl(-\int_{t_0}^{t}p(u) du\Biggr) dt= \infty
\]
are not employed.
Reviewer: R.R.Akhmerov (Novosibirsk)
MSC:
| 34K11 | Oscillation theory of functional-differential equations |
| 34K12 | Growth, boundedness, comparison of solutions to functional-differential equations |
| 34K25 | Asymptotic theory of functional-differential equations |
Keywords:
retarded functional-differential equation; \(n\)th-order equation; comparison principle; oscillation criteriaReferences:
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