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On a class of linear \(n\)-th order differential equations. (English) Zbl 0685.34034
Linear time-varying differential equations of the form \[ y^{(n)}(t)+\sum^{n}_{i=2}p_ i(t)y^{(n-i)}(t)=0,\quad t\in [a,\infty),\quad a\in {\mathbb{R}}, \] with \(p_ i(\cdot)\) real-valued and continuous are considered. Under certain assumptions, existence of solutions without zeros, a comparison theorem, the existence of a bundle of solutions, and properties of nonoscillatory (i.e. the set of zeros is bounded) is presented.
Reviewer: A.Ilchmann

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A30 Linear ordinary differential equations and systems
Full Text: EuDML
[1] Чантурия Т. А.: О колеблемости решений линейных дифференциальных уравнений высших порядков. Доклады семинара Инст. Прикл. Мат.им. И. Н. Векуа,Тбилисского гос.унив. 16 (1982), 1-74. · Zbl 1171.03330
[2] Elias U.: Nonoscillation and Eventual disconjugacy. Proc. Amer. Math. Soc. 66 (1977), 269-275. · Zbl 0367.34024
[3] Hartman Ph:. : Principal Solutions of Disconjugate \(n\)-th Order Linear Differential Equations. Amer. J. Math. 91 (1969), 306-362. · Zbl 0184.11603
[4] Greguš M.: Third Order Linear Differential Equations. D. Reidel Publishing Co., Dordrecht, 1987. · Zbl 0602.34005
[5] Кигурадзе И. Т.: Некоторые сингулярные краевые задачи для обыкновенных дифференциальных уравнений. Издат. Тбилисского гос. унив., Тбилиси 1975. · Zbl 1159.86300
[6] Лєєун А. Ю.: Неосцилляция решений уравнения \(X^{(n)} + p_1(t) x^{(n-1)} + \ldots + p_n(t) x = 0\). Усд. Мат. Наук, t. 24 (1969), 43-96.
[7] Medved’ M.: Sufficient Condition for the Non-Oscillation of the Non-Homogeneous Linear \(n\)-th Order Differential Equation. Mat. Čas. 18 (1968), 99-104.
[8] Regenda J.: Oscillatory and Nonoscillatory Properties of Solutions of the Differential Equation \(y^{(4)} + P(t)y" + Q(t)y = 0\). Math. Slovaca 28 (1978), 329-342. · Zbl 0406.34041
[9] Regenda J.: On the Oscillation of Solutions of a Class of Linear Fourth Order Differential Equations. Czech. Math. J. 33 (108) (1983), 141-148. · Zbl 0547.34023
[10] Regenda J.: Oscillation Theorems for a Class of Linear Fourth Order Differential Equations. Czech. Math. J. 34 (109) (1984), 113-120. · Zbl 0542.34030
[11] Regenda J.: Oscillation Criteria for Differential Equation \(y^{(4)} + P(t)y"+R(t)y' + Q(t)y=0\). Math. Slovaca 34 (1984),419-425. · Zbl 0598.34028
[12] Šeda V.: Nonoscillatory Solutions of Differential Equations With Deviating Argument. Czech. Math. J. 36 (111) (1986), 93-107. · Zbl 0603.34064
[13] Trench W. F.: Canonical Forms and Principal Systems for General Disconjugate Equations. Trans. Amer. Math. Soc. 189 (1974), 319-327. · Zbl 0289.34051
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