## Oscillation criteria and growth of nonoscillatory solutions of even order ordinary and delay-differential equations

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- by R. Grimmer
- Trans. Amer. Math. Soc.
**198**(1974), 215-228 - DOI: https://doi.org/10.1090/S0002-9947-1974-0348227-0
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## Abstract:

A number of results are presented on oscillation and growth of nonoscillatory solutions of the differential equation ${x^{(n)}}(t) + f(t,x(t)) = 0$. It is shown that a nonoscillatory solution satisfies a first-order integral inequality while its $(n - 1)$st derivative satisfies a first-order differential inequality. By applying the comparison principle, results are obtained by analyzing the two associated first-order scalar differential equations. In the last section it is shown that these results can be easily extended to delay-differential equations.## References

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## Bibliographic Information

- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**198**(1974), 215-228 - MSC: Primary 34K15; Secondary 34C10
- DOI: https://doi.org/10.1090/S0002-9947-1974-0348227-0
- MathSciNet review: 0348227