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Oscillation criteria for a forced second-order linear differential equation. (English) Zbl 0922.34029
The paper deals with the forced second-order linear differential equation $$(p(t)y')'+q(t)y=f(t), \quad t\in [0,\infty), \tag 1$$ 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 {\it 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 $(p(t)y')'+ q(t)y=0$ is nonoscillatory. Two examples are given to show how the results can be applied where previous results are inconclusive.

34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
Full Text: DOI
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