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The upper and lower bounds on non-real eigenvalues of indefinite Sturm-Liouville problems


Authors: Jiangang Qi, Bing Xie and Shaozhu Chen
Journal: Proc. Amer. Math. Soc. 144 (2016), 547-559
MSC (2010): Primary 34B24, 34L15; Secondary 47B50
DOI: https://doi.org/10.1090/proc/12854
Published electronically: July 29, 2015
MathSciNet review: 3430833
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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.


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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
Email: xiebing@sdu.edu.cn

Shaozhu Chen
Affiliation: Department of Mathematics, Shandong University, Weihai 264209, People’s Republic of China
Email: szchen@sdu.edu.cn

DOI: https://doi.org/10.1090/proc/12854
Keywords: Indefinite Sturm-Liouville problem, Krein space, non-real eigenvalue, a priori bounds.
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
Article copyright: © Copyright 2015 American Mathematical Society