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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
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