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

Abstract

We studied the global stability and boundedness results of third-order nonlinear differential equations of the form x + psi(x,(x) over dot,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 equivalent to 0 and the other with P not equal 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.