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Oscillation theorems for linear differential equations of second order. (English) Zbl 0661.34030

Some new oscillation criteria are given for second order ordinary differential equations of the form \(x''(t)+a(t)x(t)=0,\) \(t\geq t_ 0\), where a is a continuous real-valued function on the interval \([t_ 0,\infty)\) without any restriction on its sign. These criteria extend and improve previous oscillations results due to I. V. Kamenev [Mat. Zametki 23, 249-251 (1978; Zbl 0386.34032)] and J. Yan [Proc. Am. Math. Soc. 98, 276-282 (1986; Zbl 0622.34027)]. The results obtained can be applied in some cases in which other known oscillation theorems are not applicable.
Reviewer: Ch.G.Philos

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A30 Linear ordinary differential equations and systems
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