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

Muzaffer Ateş

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: 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.

Date: 2013
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https://doi.org/10.1155/2013/103260

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:103260

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