Inequalities for eigenvalues of the buckling problem of arbitrary order

2010/10/12 by Qing-Ming Cheng, Xuerong Qi, Cheng, Qing-Ming +5
Computer Science · Engineering · Mathematics · #35P15 #53C20 #53C42 #58G25 #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #Differential Geometry (math.DG) #FOS: Mathematics #Mechanical Behavior of Composites #math.DG #msc:35P15 #msc:53C20 #msc:53C42 #msc:58G25

paper · pdf · doi:10.48550/arxiv.1010.2327

20 pages

arxiv created 2010/10/12 · openalex publication_date 2010/10/12 · arxiv updated 2010/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies eigenvalues of the buckling problem of arbitrary order on bounded domains in Euclidean spaces and spheres. We prove universal bounds for the k-th eigenvalue in terms of the lower ones independent of the domains. Our results strengthen the recent work in [28] and generalize Cheng-Yang's recent estimates [16] on the buckling eigenvalues of order two to arbitrary order.

Citations

• Universal bounds on eigenvalues of the buckling problem on spherical domains
• Universal bounds for eigenvalues of a buckling problem II

Related

• Inequalities for Eigenvalues of the Buckling Problem of Higher Orders
• Universal Inequalities for Eigenvalues of the Buckling Problem of Arbitrary Order
• Eigenvalues of the buckling problem of arbitrary order on bounded domains of \mathbbM×ℝ
• Universal bounds for eigenvalues of a buckling problem II
• Universal bounds on eigenvalues of the buckling problem on spherical domains