Asymptotic behaviour of nonoscillatory solutions of the fourth order differential equations

Sobalová, Monika

Archivum mathematicum, Tome 38 (2002) no. 4, pp. 311-317.

Résumé

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 $.

Détail

Classification : 34C10, 34D05
Keywords: the fourth order differential equation; nonoscillatory solution