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A note on oscillation and nonoscillation criteria for fourth order linear differential equations. (English) Zbl 0539.34022
The author studies the equation (L) \(y^{(4)}+P(t)y''+Q(t)y=0\), where P(t)(\(\leq 0)\), Q(t)(\(\leq 0)\) are continuous functions on \(I=[a,\infty)\), \(a\in R\) and Q(t) is not identically zero on any subinterval of I. He proves that (L) is nonoscillatory if \(u^{(4)}+[P(t)+Q(t)]u=0\) is nonoscillatory
Reviewer: P.Marusiak

MSC:
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A30 Linear ordinary differential equations and systems
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References:
[1] HOWARD H.: Oscillation criteria for fourth order linear differential equations. Trans. Amer. Math. Soc., 96, 1960, 296-311. · Zbl 0094.28503
[2] LEIGHTON W., NEHARI Z.: On the oscillation of solutions of self-adjoint linear differential equations of the fourth order. Trans. Amer. Math. Soc., 89, 1958, 325-377. · Zbl 0084.08104
[3] REGENDA J.: Oscillation and nonoscillation properties of the solutions of the differential equation y(4) + P(t)y”+Q(t)Y = 0. Math. Slov., 29, 1978, 329-342. · Zbl 0406.34041
[4] REGENDA J.: Oscillation criteria for fourth-order linear differential equations. Math. Slov., 29, 1978, 3-16. · Zbl 0408.34032
[5] SWANSON C. A.: Comparison and Oscillation Theory of Linear Differential Equations. New York and London 1968. · Zbl 0191.09904
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