On the Global Stability Properties and Boundedness Results of Solutions of Third-Order Nonlinear Differential Equations

Abstract EN

We studied the global stability and boundedness results of third-order nonlinear differential equations of the form x⃛+ψ(x,x˙,x¨)x¨+f(x,x˙,x¨)=P(t,x,x˙,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≡0 and the other with P≠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.