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


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.