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

We studied the global stability and boundedness results of third-order nonlinear differential equations of the form x+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. © 2013 muzaffer ateş.