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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, tt 0 , where a is a continuous real-valued function on the interval [t 0 ,) 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:
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34A30Linear ODE and systems, general
References:
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[2]P. Hartman, On nonoscillatory linear differential equations of second order. Amer. J. Math.74, 389-400 (1952). · Zbl 0048.06602 · doi:10.2307/2372004
[3]I. V. Kamenev, An integral criterion for oscillation of linear differential equations of secondorder. Mat. Zametki23, 249-251 (1978) [Math. Notes23, 136-138 (1978)].
[4]M. K. Kwong andA. Zettl, Asymptotically constant unctions and second order linear oscillation. J. Math. Anal. Appl.93, 475-494 (1983). · Zbl 0525.34026 · doi:10.1016/0022-247X(83)90188-9
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[6]Ch. G. Philos, On a Kamenev’s integral criterion for oscillation of linear differential equations of second order. Utilitas Math.24, 277-289 (1983).
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[9]J. Yan, A note on an oscillation criterion for an equation with damped term. Proc. Amer.Math. Soc.90, 277-280 (1984). · doi:10.1090/S0002-9939-1984-0727249-3
[10]J. Yan, Oscillation theorems for second order linear differential equations with damping. Proc. Amer. Math. Soc.98, 276-282 (1986). · doi:10.1090/S0002-9939-1986-0854033-4
[11]C. C. Yeh, An oscillation criterion for second order nonlinear differential equations withfunctional arguments. J. Math. Anal. Appl.76, 72-76 (1980). · Zbl 0465.34043 · doi:10.1016/0022-247X(80)90059-1
[12]C. C. Yeh, Oscillation theorems for nonlinear second order differential equations with damped term. Proc. Amer. Math. Soc.84, 397-402 (1982). · doi:10.1090/S0002-9939-1982-0640240-9