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Estimates for lower bounds of eigenvalues of the poly-Laplacian and the quadratic polynomial operator of the Laplacian

Published online by Cambridge University Press:  03 December 2013

Qing-Ming Cheng ,
He-Jun Sun ,
Guoxin Wei  and
Lingzhong Zeng
Qing-Ming Cheng
Affiliation:
Department of Applied Mathematics, Faculty of Sciences, Fukuoka University, Fukuoka 814-0180, Japan
He-Jun Sun
Affiliation:
Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China (hejunsun@163.com)
Guoxin Wei
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, People's Republic of China
Lingzhong Zeng
Affiliation:
Department of Mathematics, Graduate School of Science and Engineering, Saga University, Saga 840-8502, Japan
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Abstract

In this paper, we investigate the Dirichlet eigenvalue problems of the poly-Laplacian with any order and the quadratic polynomial operator of the Laplacian. We give some estimates for lower bounds of the sums of their first k eigenvalues.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 6 , December 2013 , pp. 1147 - 1162
Copyright
Copyright © Royal Society of Edinburgh 2013 

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