| Title:
|
Asymptotic behaviour of nonoscillatory solutions of the fourth order differential equations (English) |
| Author:
|
Sobalová, Monika |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
38 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
311-317 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper the fourth order nonlinear differential equation $y^{(4)}+(q(t)y^{\prime })^{\prime }+r(t)f(y)=0$, where $q\in C^{1}( [0,\infty ))$, $r\in C^{0}( [0,\infty ))$, $f\in C^{0}(R)$, $r\ge 0$ and $f(x)x>0$ for $x\ne 0$ is considered. We investigate the asymptotic behaviour of nonoscillatory solutions and give sufficient conditions under which all nonoscillatory solutions either are unbounded or tend to zero for $t\rightarrow \infty $. (English) |
| Keyword:
|
the fourth order differential equation |
| Keyword:
|
nonoscillatory solution |
| MSC:
|
34C10 |
| MSC:
|
34D05 |
| idZBL:
|
Zbl 1090.34028 |
| idMR:
|
MR1942661 |
| . |
| Date available:
|
2008-06-06T22:31:08Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107845 |
| . |
| Reference:
|
[1] Bartušek M., Sobalová M.: On Nonoscillatory solutions of the 4th Order Differential Equations.Dynam. Syst. Appl., Proceedings of Dynam. Systems and Applications 3 (2001), 61–68. |
| Reference:
|
[2] Cecchi M., Došlá Z., Marini M.: On Third Order Differential Equations with Property A and B.J. Math. Anal. Appl. 231 (1999), 509–525. Zbl 0926.34025, MR 1669163 |
| Reference:
|
[3] Kiguradze I.: An Oscillation Criterion for a Class of Ordinary Differential Equations.Differ. Uravn., Vol. 28, No 2 (1992), 207–219. Zbl 0768.34018, MR 1184921 |
| Reference:
|
[4] Kiguradze I. T., Chanturia T. A.: Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations.Nauka, Moscow (1990) (in Russian). |
| Reference:
|
[5] Škerlík A.: Oscillation Theorems for Third Order Nonlinear Differential Equations.Math. Slovaca 42 (1992), 471–484. Zbl 0760.34031, MR 1195041 |
| . |
