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A note on the oscillation of solutions of the differential equation \(y''+\lambda q(t)y=0\) with an almost periodic coefficient. (English) Zbl 0615.34043

Let \(q\neq 0\) be a (real) almost periodic function. The following theorem is proved: The equation \(y''+\lambda q(t)y=0\) is oscillatory for every \(\lambda\), \(\lambda\in R-\{0\}\) if and only if \(M\{q\}=0\) (M\(\{\) \(q\}\) is the mean value of the function q).

MSC:

34C99 Qualitative theory for ordinary differential equations
34A30 Linear ordinary differential equations and systems
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References:

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