| Title:
|
Asymptotic properties of trinomial delay differential equations (English) |
| Author:
|
Džurina, Jozef |
| Author:
|
Kotorová, Renáta |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
149-158 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this paper is to study asymptotic properties of the solutions of the third order delay differential equation
\[ \Big (\frac{1}{r(t)}\,y^{\prime }(t)\Big )^{\prime \prime }-p(t)\,y^{\prime }(t)+g(t)\,y\big (\tau (t)\big )= 0\,.\ast \]
Using suitable comparison theorem we study properties of Eq. () with help of the oscillation of the second order differential equation. (English) |
| Keyword:
|
oscillation |
| Keyword:
|
property(A) |
| Keyword:
|
delay argument |
| MSC:
|
34C10 |
| MSC:
|
34K11 |
| MSC:
|
34K25 |
| idZBL:
|
Zbl 1212.34231 |
| idMR:
|
MR2432852 |
| . |
| Date available:
|
2008-07-24T13:18:04Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116932 |
| . |
| Reference:
|
[1] Bartušek, M., Cecchi, M., Došlá, Z., Marini, M.: On nonoscillatory solutions of third order nonlinear differential equations.Dyn. Syst. Appl. 9 (2000), 483–500. MR 1843694 |
| Reference:
|
[2] Bellman, R.: Stability Theory of Differential Equations.McGraw-Hill Book Company, New York-London, 1953. Zbl 0053.24705, MR 0061235 |
| Reference:
|
[3] Cecchi, M., Došlá, Z., Marini, M.: On the third order differential equations with property A and B.J. Math. Anal. Appl. 231 (1999), 509–525. MR 1669163, 10.1006/jmaa.1998.6247 |
| Reference:
|
[4] Cecchi, M., Marini, M., Villari, G.: On the monotonicity property for a certain class of second order differential equations.J. Differential Equations 82 (1989), 15–27. Zbl 0694.34035, MR 1023299, 10.1016/0022-0396(89)90165-4 |
| Reference:
|
[5] Chanturia, T. A., Kiguradze, I. T.: Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations.Nauka, Moscow, 1990, in Russian. |
| Reference:
|
[6] Džurina, J.: Asymptotic properties of the third order delay differential equations.Nonlinear Analysis 26 (1996), 33–39. MR 1354789, 10.1016/0362-546X(94)00239-E |
| Reference:
|
[7] Džurina, J.: Comparison theorems for functional differential equations.EDIS Žilina, 2002. |
| Reference:
|
[8] Džurina, J.: Comparison theorems for nonlinear ODE’s.Math. Slovaca 1992 (42), 299–315. MR 1182960 |
| Reference:
|
[9] Erbe, L.: Existence of oscillatory solutions and asymptotic behavior for a class of third order linear differential equation.Pacific J. Math. 1976 (64), 369–385. MR 0435508 |
| Reference:
|
[10] Hartman, P.: Ordinary Differential Equations.John Wiley & Sons, New York - London - Sydney, 1964. Zbl 0125.32102, MR 0171038 |
| Reference:
|
[11] Jones, G. D.: An asymptotic property of solutions $y^{\prime \prime \prime }+p(x)y^{\prime }+q(x)$ $y=0$.Pacific J. Math. 47 (1973), 135–138. MR 0326065 |
| Reference:
|
[12] Kiguradze, I. T.: On the oscillation of solutions of the equation $\frac{d^mu}{dt^m} +a(t)|u|^n sign\,u = 0$.Mat. Sb. 65 (1964), 172–187, in Russian. Zbl 0135.14302, MR 0173060 |
| Reference:
|
[13] Kusano, T., Naito, M.: 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:
|
[14] Kusano, T., Naito, M., Tanaka, K.: 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:
|
[15] Lacková, D.: The asymptotic properties of the solutions of $n$-th order neutral differential equations.Arch. Math. (Brno) 39 (2003), 179–185. |
| Reference:
|
[16] Lazer, A. C.: The behavior of solutions of the differential equation $y^{\prime \prime \prime }+p(x)y^{\prime }+q(x)\,y=0$.Pacific J. Math. 17 (1966), 435–466. Zbl 0143.31501, MR 0193332, 10.2140/pjm.1966.17.435 |
| Reference:
|
[17] Mahfoud, W. E.: 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:
|
[18] Parhi, N., Padhi, S.: On asymptotic behaviour of delay differential equations of third order.Nonlinear Anal. 34 (1998), 391–403. MR 1635717, 10.1016/S0362-546X(97)00600-7 |
| Reference:
|
[19] Skerlík, A.: Integral criteria of oscillation for the third order linear differential equations.Math. Slovaca 45 (1995), 403–412. MR 1387057 |
| Reference:
|
[20] Trench, W. F.: Canonical forms and principal systems for general disconjugate equations.Trans. Amer. Math. Soc. 189 (1974), 319–327. Zbl 0289.34051, MR 0330632, 10.1090/S0002-9947-1974-0330632-X |
| Reference:
|
[21] Trench, W. F.: Eventual disconjugacy of linear differential equation.Proc. Amer. Math. Soc. 83 (1983), 461–466. MR 0715867, 10.1090/S0002-9939-1983-0715867-7 |
| . |
