On the asymptotic behaviour of solutions of certain non-autonomous differential equations (Q5916485)

The authors study the behaviour of the solutions of the nonautonomous differential equation \[ x^{(4)}+f(t,x,\dot x,\ddot x,\dddot x)\dddot x+\Phi(t,\dot x,\ddot x)+g(t,x,\dot x)+d(t)h(x)= P(t,x, \dot x,\dddot x)\tag{*} \] as \(t\to\infty\), where \(f,\Phi,g,d,h\), and \(P\) are real-valued functions. There are given sufficient conditions for uniform boundedness and convergence to zero of all solutions of (*). The results given here generalize some earlier results and are based on the construction of a Lyapunov function. The technique used is the same as in \textit{A. I. Sadek} [Math. Jap. 45, No. 3, 527--540 (1997; Zbl 0896.34044)].