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 $.
@article{107845,
author = {Monika Sobalov\'a},
title = {Asymptotic behaviour of nonoscillatory solutions of the fourth order differential equations},
journal = {Archivum Mathematicum},
volume = {038},
year = {2002},
pages = {311-317},
zbl = {1090.34028},
mrnumber = {1942661},
language = {en},
url = {http://dml.mathdoc.fr/item/107845}
}
Sobalová, Monika. Asymptotic behaviour of nonoscillatory solutions of the fourth order differential equations. Archivum Mathematicum, Tome 038 (2002) pp. 311-317. http://gdmltest.u-ga.fr/item/107845/
On Nonoscillatory solutions of the 4th Order Differential Equations, Dynam. Syst. Appl., Proceedings of Dynam. Systems and Applications 3 (2001), 61–68.
On Third Order Differential Equations with Property A and B, J. Math. Anal. Appl. 231 (1999), 509–525. (1999) | MR 1669163 | Zbl 0926.34025
An Oscillation Criterion for a Class of Ordinary Differential Equations, Differ. Uravn., Vol. 28, No 2 (1992), 207–219. (1992) | MR 1184921 | Zbl 0768.34018
Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations, Nauka, Moscow (1990) (in Russian). (1990)
Oscillation Theorems for Third Order Nonlinear Differential Equations, Math. Slovaca 42 (1992), 471–484. (1992) | MR 1195041 | Zbl 0760.34031