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

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• 作者：Makhlouf Amar ; ^{makhloufamar@yahoo.fr} ; Debbabi Djamel ^{djamel.debbabi@gmail.com}
• 关键词：Periodic solution ; Third order differential equations ; Averaging theory
• 刊名：Chaos, Solitons & Fractals
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：94
• 期：Complete
• 页码：112-118
• 全文大小：430 K
• 卷排序：94

文摘

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)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.