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.


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


Zbl 0777.34023
Full Text: DOI


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