We prove \(L^r\)-estimates on periodic solutions of periodically forced, linearly damped mechanical systems with polynomially bounded potentials. The estimates are applied to obtain a nonexistence result of periodic solutions in bounded domains, depending on an upper bound on the gradient of the potential. The results are illustrated on examples.

中文翻译：

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有界域中强迫阻尼势能系统周期轨道的不存在

我们证明\（L ^ r \）-估计具有多项式有界电势的周期性强迫线性阻尼机械系统的周期解。应用估计以获得有界域中周期解的不存在结果，这取决于势梯度的上限。结果在示例中说明。