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Oscillation of second order delay and ordinary differential equation. (English) Zbl 0543.34054
Two oscillation criteria are given for the equation $$u''(t)+p(t)u(h(t))=0,$$ where p(t)$$\geq 0$$, h(t)$$\leq t$$ and h(t)$$\to \infty$$ as $$t\to \infty$$. For $$h(t)=t$$ the first criterion seems to be already known.
Reviewer: M.M.Konstantinov

##### MSC:
 34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument) 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
##### Keywords:
oscillation criteria
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##### References:
 [1] T. A. Canturija: Integral criteria of oscillation of solutions of linear differential equations of higher order. (Russian). Differ urav., XVI, 3, 1980, 470-482. [2] L. Erbe: Oscillation criteria for second order nonlinear delay equations. Canad. Math. Bull. 16 (1), 1973, 49-56. · Zbl 0272.34095 [3] J. G. Mikusiňski: On Fite’s oscillation theorems. Colloq. Math. II, 1949, 34-39. · Zbl 0039.31302 [4] V. N. Ševelo N. V. Varech: On certain properties of solutions of differential equations with a delay. (Ukrainian) UMŽ, 24, 6, 1972, 807-813. [5] A. Vintner: A criterion of oscillatory stability. Quart. Appl. Math. 7, 1, 1949, 115-117.
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