Bound of solutions to third-order nonlinear differential equations with bounded delay.

*(English)*Zbl 1193.34139Consider the delay differential equation

under the assumption that the delay satisfies

$$0\le r\left(t\right)\le \alpha ,\phantom{\rule{1.em}{0ex}}{r}^{\text{'}}\left(t\right)\le \beta ,\phantom{\rule{1.em}{0ex}}\alpha >0,\phantom{\rule{1.em}{0ex}}0<\beta <1\xb7$$

The author gives additional conditions on $f$, $g$, $h$, $p$ such that the solution of the Cauchy problem of $(*)$ is uniformly bounded including its first and second derivative. The proof is based on the construction of a Lyapunov functional.

Reviewer: Klaus R. Schneider (Berlin)

##### MSC:

34K12 | Growth, boundedness, comparison of solutions of functional-differential equations |

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