On the global stability properties and boundedness results of solutions of third-order nonlinear differential equations (Q1789744)

Summary: We studied the global stability and boundedness results of third-order nonlinear differential equations of the form \(\dddot{x}+\psi(x,\dot x,\ddot{x})\ddot{x}+f(x,\dot{x},\ddot{x})=P(t,x,\dot x,\ddot{x})\). Particular cases of this equation have been studied by many authors over years. However, this particular form is a generalization of the earlier ones. A Lyapunov function was used for the proofs of the two main theorems: one with \(P\equiv 0\) and the other with \(P\neq 0\). The results in this paper generalize those of other authors who have studied particular cases of the differential equations. Finally, a concrete example is given to check our results.