zbMATH — the first resource for mathematics

Stability and boundedness of solutions to certain fourth-order differential equations. (English) Zbl 1096.34024
Summary: We give criteria for the asymptotic stability and boundedness of solutions to the nonlinear fourth-order ordinary differential equation
$x^{(4)}+\varphi (\ddot{x})\dddot{x}+f(x,\dot{x}) \ddot{x}+g(\dot{x})+h(x)=p(t,x,\dot{x},\ddot{x},\dddot{x})\,,$
when $$p\equiv 0$$ and when $$p\neq 0$$. Our results include and improve some well-known results in the literature.

MSC:
 34C11 Growth and boundedness of solutions to ordinary differential equations 34D20 Stability of solutions to ordinary differential equations
Full Text: