Optimal upper bounds for the eigenvalue ratios of one-dimensional $p$-Laplacian
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- by Chao-Zhong Chen, C. K. Law, Wei-Cheng Lian and Wei-Chuan Wang PDF
- Proc. Amer. Math. Soc. 141 (2013), 883-893 Request permission
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.References
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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
- 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
- © Copyright 2012 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 141 (2013), 883-893
- MSC (2010): Primary 34A34, 34L15
- DOI: https://doi.org/10.1090/S0002-9939-2012-11365-6
- MathSciNet review: 3003681