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具有一般非线性弹性力和广义阻尼力的相对转动非线性系统的周期解问题
The p erio dic solution problem of a relative rotation nonlinear system with nonlinear elastic force and generalized damping force
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摘要: 讨论了一类相对转动非线性动力系统的周期解问题。首先建立了一类具有一般非线性弹性力、广义阻尼力和强迫周期力项的相对转动非线性动力系统；其次得到了对应自治系统的周期解不存在性结果，以及运用Mawhin重合度理论得到了该模型的周期解存在性结果，推广了已有的结果；最后举例证明本文结果的正确性。Abstract: The periodic solution problem of a relative rotation nonlinear system is considered. Firstly, the relative rotation nonlinear dynamic system is established, which contains nonlinear elastic force, commonly damped force and forcing periodic force. Secondly, the result about the nonexistence of periodic solution of the corresponding autonomous system is obtained, and some results about the existence of periodic solutions of the system are obtained by using the continuation theorem of coincidence degree theory. The significance is that we generalize the existing results of the literature. Finally an example is given to illustrate that our results are right.
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