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Proceedings of the American Mathematical Society

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On the existence of stable periodic solutions of differential equations of Duffing type


Authors: A. C. Lazer and P. J. McKenna
Journal: Proc. Amer. Math. Soc. 110 (1990), 125-133
MSC: Primary 34C25; Secondary 34D20, 70K40
MathSciNet review: 1013974
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Abstract: We consider a second-order differential equation periodic in $ t$ with period $ T > 0$ and with linear damping. Bounds are given for the derivative of the restoring force which will guarantee the existence and uniqueness of a $ T$-periodic solution such that the unique $ T$-periodic solution is asymptotically stable. These conditions also rule out the existence of additional periodic solutions which are subharmonics of order 2.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1013974-9
Keywords: Contraction mapping theorem, fundamental matrix, characteristic multipliers, asymptotically, exponentially stable
Article copyright: © Copyright 1990 American Mathematical Society