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Asymptotic properties of the third order delay differential equations. (English) Zbl 0840.34076

The author using comparison techniques investigates the oscillatory and nonoscillatory properties of the third-order delay differential equation \(y'''(t)- p(t) y'(t)+ g(t) y(\tau(t))= 0\). Several criteria are given.
Reviewer: M.Lizana (Merida)

MSC:

34K11 Oscillation theory of functional-differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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References:

[1] Erbe, L., Existence of oscillatory solutions and asymptotic behavior for a class of third order linear differential equations, Pacif. J. Math., 64, 369-385 (1976) · Zbl 0339.34030
[2] Jones, G. D., An asymptotic property of solutions y‴p(x)y′q(x)y = 0, Pacif. J. Math., 47, 135-138 (1973)
[3] Lazer, A. C., The behavior of solutions of the differential equation y‴p(x)y′q(x)y = 0, Pacif. J. Math., 17, 435-466 (1966) · Zbl 0143.31501
[4] Škerlík A., Oscillatory criteria for the third order linear differential equations, Math. Slovaca (to appear).; Škerlík A., Oscillatory criteria for the third order linear differential equations, Math. Slovaca (to appear).
[5] Trench, W. F., Canonical forms and principal systems for general disconjugate equations, Trans. Am. math. Soc., 189, 319-327 (1974) · Zbl 0289.34051
[6] Kusano, T.; Naito, M.; Tanaka, K., Oscilltory and asymptotic behavior of solutions of a class of linear ordinary differential equations, (Proc. R. Soc. Edinb., 90 (1981)), 25-40
[7] Kusano, T.; Naito, M., Comparison theorems for functional differential equations with deviating arguments, J. math. Soc. Japan, 3, 509-532 (1981) · Zbl 0494.34049
[8] Chanturia, T. A.; Kiguradze, I. T., Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations (1990), Nauka: Nauka Berlin, (In Russian.) · Zbl 0719.34003
[9] Hartman, P., (Ordinary Differential Equations (1964), John Wiley & Sons: John Wiley & Sons Moscow) · Zbl 0125.32102
[10] Trench, W. F., Eventual disconjugacy of linear differential equation, (Proc. Am. math. Soc., 83 (1983)), 461-466 · Zbl 0529.34041
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