The upper and lower bounds on non-real eigenvalues of indefinite Sturm-Liouville problems
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Abstract:
The present paper gives a priori upper and lower bounds on non-real eigenvalues of regular indefinite Sturm-Liouville problems only under the integrability conditions. More generally, a lower bound on non-real eigenvalues of the self-adjoint operator in Krein space is obtained.References
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Additional Information
- Jiangang Qi
- Affiliation: Department of Mathematics, Shandong University, Weihai 264209, People’s Republic of China
- Email: qijiangang@sdu.edu.cn
- Bing Xie
- Affiliation: Department of Mathematics, Shandong University, Weihai 264209, People’s Republic of China
- MR Author ID: 943304
- Email: xiebing@sdu.edu.cn
- Shaozhu Chen
- Affiliation: Department of Mathematics, Shandong University, Weihai 264209, People’s Republic of China
- MR Author ID: 230820
- Email: szchen@sdu.edu.cn
- Received by editor(s): September 28, 2014
- Received by editor(s) in revised form: December 22, 2014
- Published electronically: July 29, 2015
- Additional Notes: The first author was supported in part by the NSF of Shandong Province Grant #ZR2012AM002, and the NSF of China Grants #11471191 and #11101241.
The second author is the corresponding author
The third author was supported in part by the NSF of China Grant #11271229 and the SFPIP of Shandong Province Grant #201301010. - Communicated by: Nimish Shah
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 547-559
- MSC (2010): Primary 34B24, 34L15; Secondary 47B50
- DOI: https://doi.org/10.1090/proc/12854
- MathSciNet review: 3430833