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.