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

Grimmer, R.

doi:10.1090/S0002-9947-1974-0348227-0

Oscillation criteria and growth of nonoscillatory solutions of even order ordinary and delay-differential equations
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Trans. Amer. Math. Soc. 198 (1974), 215-228 Request permission

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.

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