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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 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.

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

Citations:

Zbl 0777.34023
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References:

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