##
Asymptotic Behaviour of Nonoscillatory Solutions of the Fourth Order Differential
Equations

##
*Monika Sobalova*

**Address.** Department of Mathematics, Faculty of Science, Masaryk
University, Janackovo nam. 2a, 662 95 Brno,

Czech Republic
**E-mail: **sobalova@math.muni.cz

**Abstract. **In the paper the fourth order nonlinear differential
equation

$y^{(4)}+(q(t)y')'+r(t)f(y)=0$, where $q\in C^{1}( [0,\infty ))$,

$r\in C^{0}( [0,\infty ))$, $f\in C^{0}(R)$, $r\geq 0$ and $f(x)x>0$
for $x\not= 0$

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 $t\to\infty$.

**AMSclassification.** 34C10.

**Keywords.** The fourth order differential equation, nonoscillatory
solution.