Periodic solutions of some classes of continuous third-order differential equations

Makhlouf Amar and Debbabi Djamel

Chaos, Solitons & Fractals, 2017, vol. 94, issue C, 112-118

Abstract: We study the periodic solutions of the third-order differential equations of the form x⃛±xn=μf(t), or x⃛±|x|n=μf(t), where n=2,3,…,f(t) is a continuous T− periodic function such that ∫0Tf(t)dt≠0, and µ is a positive small parameter. Note that the differential equations x⃛±xn=μf(t) are only continuous in t and smooth in x, and that the differential equations x⃛±|x|n=μf(t) are only continuous in t and locally-Lipschitz in x. We also study the stability of the periodic solutions.

Keywords: Periodic solution; Third order differential equations; Averaging theory (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:94:y:2017:i:c:p:112-118

DOI: 10.1016/j.chaos.2016.11.012

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