Oscillation criteria for a forced second-order linear differential equation.

*(English)*Zbl 0922.34029The paper deals with the forced second-order linear differential equation

$${\left(p\left(t\right){y}^{\text{'}}\right)}^{\text{'}}+q\left(t\right)y=f\left(t\right),\phantom{\rule{1.em}{0ex}}t\in [0,\infty ),\phantom{\rule{2.em}{0ex}}\left(1\right)$$

where $p>0$, $q,f$ are continuous functions. The author presents two oscillation criteria for equation (1) that do not assume that $q$ and $f$ be of definite sign.

In theorem 1, a result of *M.A. El-Sayed* [Proc. Am. Math. Soc. 118, 813-817 (1993; Zbl 0777.34023)] is extended. The second criterion is derived under the assumption that the unforced equation ${\left(p\left(t\right){y}^{\text{'}}\right)}^{\text{'}}+q\left(t\right)y=0$ is nonoscillatory.

Two examples are given to show how the results can be applied where previous results are inconclusive.

Reviewer: J.Ohriska (Košice)

##### MSC:

34C10 | Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory |