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

[摘要] We studied the global stability and boundedness results of third-order nonlinear differential equations of the formx⃛+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 formis a generalizationof the earlier ones. A Lyapunov function was used for the proofs of the two main theorems: one withP≡0and the other withP≠0. The results in this paper generalize those of other authorswhohave studied particular cases of the differential equations. Finally, a concrete example is given to check our results.

[学科分类] 应用数学