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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Universal bounds for eigenvalues of a buckling problem II


Authors: Qing-Ming Cheng and Hongcang Yang
Journal: Trans. Amer. Math. Soc. 364 (2012), 6139-6158
MSC (2010): Primary 35P15, 53C42
Published electronically: April 18, 2012
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Abstract: In this paper, we investigate universal estimates for eigenvalues of a buckling problem. For a bounded domain in a Euclidean space, we give a positive contribution for obtaining a sharp universal inequality for eigenvalues of the buckling problem. For a domain in the unit sphere, we give an important improvement on the results of Wang and Xia.


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Additional Information

Qing-Ming Cheng
Affiliation: Department of Mathematics, Graduate School of Science and Engineering, Saga University, Saga 840-8502, Japan
Address at time of publication: Department of Applied Mathematics, Faculty of Sciences, Fukuoka University, Fukuoka 814-0180, Japan
Email: cheng@fukuoka-u.ac.jp

Hongcang Yang
Affiliation: Academy of Mathematics and Systematical Sciences, Chinese Academy of Science, Beijing 100080, People’s Republic of China
Email: yanghc2@netease.com

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05662-5
PII: S 0002-9947(2012)05662-5
Keywords: Universal estimates for eigenvalues, a biharmonic operator and a buckling problem
Received by editor(s): March 3, 2011
Received by editor(s) in revised form: July 7, 2011
Published electronically: April 18, 2012
Additional Notes: The first author’s research was partially supported by a Grant-in-Aid for Scientific Research from JSPS
The second author’s research was partially supported by SF of CAS
Article copyright: © Copyright 2012 American Mathematical Society