Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
comparison theorem; property (A); canonical operator
comparison theorem; property (A); canonical operator
Summary:
In this paper we study asymptotic properties of the third order trinomial delay differential equation $$ y'''(t)-p(t)y'(t)+g(t)y(\tau (t))= 0 $$ by transforming this equation to the binomial canonical equation. The results obtained essentially improve known results in the literature. On the other hand, the set of comparison principles obtained permits to extend immediately asymptotic criteria from ordinary to delay equations.
References:
[1] Bellman, R.: Stability theory of differential equations. New York-London McGraw-Hill Book Company, XIII (1953). MR 0061235 | Zbl 0053.24705
[2] Chanturia, T. A., Kiguradze, I. T.: Asymptotic properties of solutions of nonautonomous ordinary differential equations. (1990), Nauka Moscow Russian.
[3] Džurina, J.: Asymptotic properties of the third order delay differential equations. Nonlinear Analysis 26 (1996), 33-39. DOI 10.1016/0362-546X(94)00239-E | MR 1354789
[4] Džurina, J.: Comparison theorems for functional differential equations. (2002), EDIS Zilina.
[5] Džurina, J.: Comparison theorems for nonlinear ODE's. Math. Slovaca 42 (1992), 299-315. MR 1182960 | Zbl 0760.34030
[6] Džurina, J.: Asymptotic properties of third-order differential equations with deviating argument. Czech. Math. J. 44 (1994), 163-172. MR 1257942
[7] Džurina, J.: Asymptotic properties of third order delay differential equations. Czech. Math. J. 45 (1995), 443-448. MR 1344509
[8] Erbe, L.: Existence of oscillatory solutions and asymptotic behavior for a class of third order linear differential equation. (1976), 64 Pacific J. Math. MR 0435508
[9] Hartman, P.: Ordinary differential equations. (1964), John Wiley & sons New York-London-Sydney. MR 0171038 | Zbl 0125.32102
[10] Jones, G. D.: An asymptotic property of solutions $y'''+p(x)y'+q(x)y=0$. (1973),47 Pacific J. Math. MR 0326065
[11] Kiguradze, I. T.: On the oscillation of solutions of the equation $\frac{ d^mu}{ dt^m} + a(t)|u|^n\* sign u = 0$. (1964), 65 Mat. Sb. Russian. Zbl 0135.14302
[12] Kusano, T., Naito, M.: Comparison theorems for functional differential equations with deviating arguments. (1981), 3 J. Math. Soc. Japan. MR 0620288 | Zbl 0494.34049
[13] Kusano, T., Naito, M., Tanaka, K.: Oscillatory and asymptotic behavior of solutions of a class of linear ordinary differential equations. (1981), 90 Proc. Roy. Soc. Edinburg. MR 0636062
[14] Lazer, A. C.: The behavior of solutions of the differential equation $y'''+p(x)y'+q(x)y=0$. (1966),17 Pacific J. Math. MR 0193332 | Zbl 0143.31501
[15] Mahfoud, W. E.: Comparison theorems for delay differential equations. Pacific J. Math. 83 (1979), 187-197. DOI 10.2140/pjm.1979.83.187 | MR 0555047 | Zbl 0441.34053
[16] Parhi, N., Padhi, S.: On asymptotic behaviour of delay differential equations of third order. 391-403 34 (1998), Nonlin. Anal. DOI 10.1016/S0362-546X(97)00600-7 | MR 1635717
[17] Škerlík, A.: Integral criteria of oscillation for the third order linear differential equations. Math. Slovaca 45 (1995), 403-412. MR 1387057
[18] Trench, W. F.: Canonical forms and principal systems for general disconjugate equations. (1974), 189 Trans. Amer. Math. Soc. DOI 10.1090/S0002-9947-1974-0330632-X | MR 0330632 | Zbl 0289.34051
[19] Trench, W. F.: Eventual disconjugacy of linear differential equation. (1983), 83 Proc. Amer. Math. Soc. MR 0715867
Search
Partner of
