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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),t[0,),(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:
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory