四阶椭圆微分方程组的低阶特征值不等式

doi:10.13371/j.cnki.chin.q.j.m.2026.02.002

数学季刊 ›› 2026, Vol. 41 ›› Issue (2): 128-138.doi: 10.13371/j.cnki.chin.q.j.m.2026.02.002

四阶椭圆微分方程组的低阶特征值不等式

School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210014, China)

收稿日期:2025-08-30 出版日期:2026-06-30 发布日期:2026-06-30
作者简介:WANG Lin-lin (2000-), female, native of Xuzhou, Jiangsu, postgraduate of Nanjing University of Science and Technology, engages in differential geometry; SUN He-jun (1976-), male, native of Lianyungang, Jiangsu, professor of Nanjing University of Science and Technology, Master supervisor, Ph.D, engages in differential geometry; XIAO Meng-ge (2002-), female, native of Macheng, Hubei, postgraduate of Nanjing University ofScience and Technology, engages in differential geometry.
基金资助:
Supported by National Natural Science Foundation of China (Grant No. 11001130); Fundamental Research Funds for the Central Universities (Grant No. 30917011335).

Inequalities for Lower Order Eigenvalues of Fourth-Order Elliptic System of Differential Equations

School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210014, China)

Received:2025-08-30 Online:2026-06-30 Published:2026-06-30
About author:WANG Lin-lin (2000-), female, native of Xuzhou, Jiangsu, postgraduate of Nanjing University of Science and Technology, engages in differential geometry; SUN He-jun (1976-), male, native of Lianyungang, Jiangsu, professor of Nanjing University of Science and Technology, Master supervisor, Ph.D, engages in differential geometry; XIAO Meng-ge (2002-), female, native of Macheng, Hubei, postgraduate of Nanjing University ofScience and Technology, engages in differential geometry.
Supported by:
Supported by National Natural Science Foundation of China (Grant No. 11001130); Fundamental Research Funds for the Central Universities (Grant No. 30917011335).

摘要/Abstract

摘要： In this paper, we investigate the Dirichlet eigenvalue problem of fourth-order elliptic system of differential equations on an n-dimensional Euclidean space as follows
\begin{equation*}
\left\{\begin{aligned}
&A\Delta^2\boldsymbol{u} = -\Gamma\Delta \boldsymbol{u}, && \text{in} \quad \Omega, \\
&\boldsymbol{u} = \frac{\partial \boldsymbol{u}}{\partial \boldsymbol{\nu}} = \boldsymbol{0}, && \text{on} \quad \partial \Omega,
\end{aligned}\right.
\end{equation*}
where A is a symmetric coefficient matrix and ν is the outward unit normal vector field of ∂Ω. We derive some inequalities for lower order eigenvalues of this problem. Our results cover some previous results for the buckling problem.

关键词: Eigenvalue, Inequality, Elliptic system of differential equations

Abstract: In this paper, we investigate the Dirichlet eigenvalue problem of fourth-order elliptic system of differential equations on an n-dimensional Euclidean space as follows
\begin{equation*}
\left\{\begin{aligned}
&A\Delta^2\boldsymbol{u} = -\Gamma\Delta \boldsymbol{u}, && \text{in} \quad \Omega, \\
&\boldsymbol{u} = \frac{\partial \boldsymbol{u}}{\partial \boldsymbol{\nu}} = \boldsymbol{0}, && \text{on} \quad \partial \Omega,
\end{aligned}\right.
\end{equation*}
where A is a symmetric coefficient matrix and ν is the outward unit normal vector field of ∂Ω. We derive some inequalities for lower order eigenvalues of this problem. Our results cover some previous results for the buckling problem.

Key words: Eigenvalue, Inequality, Elliptic system of differential equations

中图分类号:

O186.1

王琳琳, 孙和军, 肖梦格. 四阶椭圆微分方程组的低阶特征值不等式[J]. 数学季刊, 2026, 41(2): 128-138.

WANG Lin-lin, SUN He-jun, XIAO Meng-ge. Inequalities for Lower Order Eigenvalues of Fourth-Order Elliptic System of Differential Equations[J]. Chinese Quarterly Journal of Mathematics, 2026, 41(2): 128-138.

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四阶椭圆微分方程组的低阶特征值不等式

Inequalities for Lower Order Eigenvalues of Fourth-Order Elliptic System of Differential Equations

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