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<p>In this paper, we are devoted to the study of universal inequalities for eigenvalues of the buckling problem of arbitrary order on domains in an Euclidean space, and then establish some new universal inequalities that are different from those already present in [Jürgen Jost, Xianqing Li-Jost, Qiaoling Wang and Changyu Xia, Trans. Amer. Math. Soc. 363 (2011), no. 4, 1821–1854] and [Qing-Ming Cheng, Xuerong Qi, Qiaoling Wang and Changyu Xia, Ann. Mat. Pura Appl. (4) 197 (2018), no. 1, 211–232]. In particular, our results can reveal the relationship between the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1266_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\((k+1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-th eigenvalue and the first <i>k</i> eigenvalues relatively quickly, and some methods used in this paper might be applied to other eigenvalue problems.</p>

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Universal inequalities for eigenvalues of the buckling problem of arbitrary order on domains in an Euclidean space

  • 期刊论文

  • 发表日期：

    2025年7月11日

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  • Yue He,
  • Yiling Jin

摘要

In this paper, we are devoted to the study of universal inequalities for eigenvalues of the buckling problem of arbitrary order on domains in an Euclidean space, and then establish some new universal inequalities that are different from those already present in [Jürgen Jost, Xianqing Li-Jost, Qiaoling Wang and Changyu Xia, Trans. Amer. Math. Soc. 363 (2011), no. 4, 1821–1854] and [Qing-Ming Cheng, Xuerong Qi, Qiaoling Wang and Changyu Xia, Ann. Mat. Pura Appl. (4) 197 (2018), no. 1, 211–232]. In particular, our results can reveal the relationship between the \((k+1)\) ( k + 1 ) -th eigenvalue and the first k eigenvalues relatively quickly, and some methods used in this paper might be applied to other eigenvalue problems.