| Title: | Property (A) of $n$-th order ODE's (English) | 
| Author: | Džurina, Jozef | 
| Language: | English | 
| Journal: | Mathematica Bohemica | 
| ISSN: | 0862-7959 (print) | 
| ISSN: | 2464-7136 (online) | 
| Volume: | 122 | 
| Issue: | 4 | 
| Year: | 1997 | 
| Pages: | 349-356 | 
| Summary lang: | English | 
| . | 
| Category: | math | 
| . | 
| Summary: | The aim of this paper is to deduce oscillatory and asymptotic behavior of the solutions of the ordinary differential equation L_nu(t)+p(t)u(t)=0. (English) | 
| Keyword: | property (A) of ODE's | 
| Keyword: | oscillatory behavior | 
| Keyword: | solutions | 
| Keyword: | ordinary differential equations | 
| Keyword: | quasiderivatives | 
| Keyword: | binomial equation | 
| Keyword: | delay-differential equation | 
| Keyword: | differential inequalities | 
| Keyword: | nonoscillatory solutions | 
| MSC: | 34C10 | 
| MSC: | 34C11 | 
| MSC: | 34D05 | 
| idZBL: | Zbl 0903.34031 | 
| idMR: | MR1489395 | 
| DOI: | 10.21136/MB.1997.126218 | 
| . | 
| Date available: | 2009-09-24T21:27:18Z | 
| Last updated: | 2020-07-29 | 
| Stable URL: | http://hdl.handle.net/10338.dmlcz/126218 | 
| . | 
| Reference: | [1] T. A. Chanturia, I. T. Kiguradze: Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations.Nauka, Moscow, 1990. (In Russian.) | 
| Reference: | [2] J. Džurina: Comparison theorems for functional differential equations.Math. Nachrichten 164 (1993), 13-22. MR 1251452, 10.1002/mana.19931640103 | 
| Reference: | [3] K. E. Foster, R. C. Grimmer: Nonoscillatory solutions of higher order differential equations.J. Math. Anal. Appl. 71 (1979), 1-17. Zbl 0428.34029, MR 0545858, 10.1016/0022-247X(79)90214-2 | 
| Reference: | [4] P. Hartman, A. Wintner: Linear differential and difference equations with monotone solutions.Amer. J. Math. 75 (1953), 731-743. Zbl 0051.07105, MR 0057404, 10.2307/2372548 | 
| Reference: | [5] T. Kusano, M. Naito: Comparison theorems for functional differential equations with deviating arguments.J. Math. Soc. Japan 3 (1981), 509-532. Zbl 0494.34049, MR 0620288, 10.2969/jmsj/03330509 | 
| Reference: | [6] T. Kusano M. Naito, K. Tanaka: Oscillatory and asymptotic behavior of solutions of a class of linear ordinary differential equations.Proc. Roy. Soc. Edinburg. 90 (1981), 25-40. MR 0636062 | 
| Reference: | [7] T. Kusano, M. Naito: Oscillation criteria for general ordinary differential equations.Pacific J. Math. 92 (1981), 345-355. MR 0618070, 10.2140/pjm.1981.92.345 | 
| Reference: | [8] D. Knežo, V. Šoltés: Existence and properties of nonoscillation solutions of third order differential equations.Fasciculi Math. 25 (1995), 63-74. MR 1339626 | 
| Reference: | [9] Š. Kulcsár: Boundedness convergence and global stability of solution of a nonlinear differential equations of the second order.Publ. Math. 37 (1990), 193-201. MR 1082298 | 
| Reference: | [10] G. S. Ladde V. Lakshmikantham B. G. Zhang: Oscillation Theory of Differential Equations with Deviating Arguments.Dekker, New York, 1987. MR 1017244 | 
| Reference: | [11] D. L. Lovelady: An asymptotic analysis of an odd order linear differential equation.Pacific J. Math. 57 (1975), 475-480. Zbl 0305.34054, MR 0379985, 10.2140/pjm.1975.57.475 | 
| Reference: | [12] D. L. Lovelady: Oscillation of a class of odd order linear differential equations.Hiroshima Math. J. 5 (1975), 371-383. MR 0387722, 10.32917/hmj/1206136533 | 
| Reference: | [13] W. E. Mahfoud: Comparison theorems for delay differential equations.Pacific J. Math. 83 (1979), 187-197. Zbl 0441.34053, MR 0555047, 10.2140/pjm.1979.83.187 | 
| Reference: | [14] W. E. Mahfoud: Characterization of oscillation of solutions of the delay   equation $x^{(n)} (t) +a(t)f(x[q(t)]) = 0.J. Differential Equations 28 (1978), 437-451. MR 0499605, 10.1016/0022-0396(78)90138-9 | 
| Reference: | [15] M. Naito: On strong oscillation of retarded differential equations.Hiroshima Math. J. vol 11 (1981), 553-560. Zbl 0512.34056, MR 0635038, 10.32917/hmj/1206133990 | 
| Reference: | [16] Ch. G. Philos, Y. G. Sficas: Oscillatory and asymptotic behavior of second and third order retarded differential equations.Czechoslovak Math. J. 32 (1982), 169-182. Zbl 0507.34062, MR 0654054 | 
| Reference: | [17] M. Růžičková, E. Špániková: Oscillation theorems for neutral differential equations with the quasi-derivatives.Arch. Math. 30 (1994), 293-300. MR 1322574 | 
| Reference: | [18] W. F. Trench: Oscillation properties of perturbed disconjugate equations.Proc. Amer. Math. Soc. 52 (1975), 147-155. Zbl 0321.34027, MR 0379987, 10.1090/S0002-9939-1975-0379987-7 | 
| . |