In this paper, we study the universal inequalities for eigenvalues of a clamped plate problem, and establish some new universal inequalities that are different from those already present in the literature, such as (Wang and Xia J. Funct. Anal. 245(1), 334-352 2007), (Wang and Xia Calc. Var. Partial Differential 653 Equations 40(1-2), 273-289 2011), (Chen, Zheng, and Lu Pacific J. Math. 255(1), 41-54 2012), and so on. In particular, our results can reveal the relationship between the \((k+1)\)-th eigenvalue and the first k eigenvalues relatively quickly.

中文翻译：

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夹紧板问题特征值的新通用不等式

在本文中，我们研究了夹紧板问题特征值的普遍不等式，并建立了一些与文献中已有的不同的新普遍不等式，例如（Wang and Xia J. Funct. Anal. 245(1) , 334-352 2007), (Wang 和 Xia Calc. Var. 偏微分 653 方程 40(1-2), 273-289 2011), (Chen, Cheng, 和 Lu Pacific J. Math. 255(1), 41 -54 2012），等等。特别是，我们的结果可以相对快速地揭示第\((k+1)\)个特征值和前k 个特征值之间的关系。