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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Optimal upper bounds for the eigenvalue ratios of one-dimensional $ p$-Laplacian


Authors: Chao-Zhong Chen, C. K. Law, Wei-Cheng Lian and Wei-Chuan Wang
Journal: Proc. Amer. Math. Soc. 141 (2013), 883-893
MSC (2010): Primary 34A34, 34L15
Published electronically: July 5, 2012
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Abstract: We give optimal upper bounds for the Dirichlet and Neumann eigenvalue ratios of the one-dimensional $ p$-Laplacian with nonnegative potentials. In case the potential is single-well, the upper bound for the Dirichlet eigenvalue ratios can be further refined.


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Additional Information

Chao-Zhong Chen
Affiliation: Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan, Republic of China

C. K. Law
Affiliation: Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan – and – National Center for Theoretical Sciences, Taiwan, Republic of China
Email: law@math.nsysu.edu.tw

Wei-Cheng Lian
Affiliation: Department of Information Management, National Kaohsiung Marine University, Kaohsiung 811, Taiwan, Republic of China
Email: wclian@mail.nkmu.edu.tw

Wei-Chuan Wang
Affiliation: Department of Mathematics, National Changhua University of Education, Changhua 500, Taiwan, Republic of China
Email: wangwc@math.nsysu.edu.tw, feymann@ms39.hinet.net

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11365-6
PII: S 0002-9939(2012)11365-6
Keywords: $p$-Laplacian, eigenvalue ratio, single-well, generalized Prüfer substitution
Received by editor(s): June 6, 2009
Received by editor(s) in revised form: July 6, 2011, and July 12, 2011
Published electronically: July 5, 2012
Additional Notes: The second and third authors were partially supported by the National Science Council, Taiwan, R.O.C., under contract numbers NSC 97-2115-M-110-005-MY2 and NSC 98-2115-M-022-001
Communicated by: Yingfei Yi
Article copyright: © Copyright 2012 American Mathematical Society