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A priori bounds and existence of non-real eigenvalues for singular indefinite Sturm–Liouville problems with limit-circle type endpoints

Part of: Ordinary differential operators Boundary value problems Special classes of linear operators

Published online by Cambridge University Press:  07 June 2019

Fu Sun  and
Jiangang Qi
Fu Sun
Affiliation:
Department of Mathematics, Shandong University(Weihai), Weihai264209, P. R. China (sfmath@163.com; qjg816@163.com)
Jiangang Qi
Affiliation:
Department of Mathematics, Shandong University(Weihai), Weihai264209, P. R. China (sfmath@163.com; qjg816@163.com)
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Abstract

The present paper deals with non-real eigenvalues of singular indefinite Sturm–Liouville problems with limit-circle type endpoints. A priori bounds and the existence of non-real eigenvalues of the problem associated with a special separated boundary condition are obtained.

Keywords

indefiniteSturm–Liouville problemnon-real eigenvaluea priori bounds

MSC classification

Primary: 34B24: Sturm-Liouville theory
Secondary: 34L15: Eigenvalues, estimation of eigenvalues, upper and lower bounds 47B50: Operators on spaces with an indefinite metric
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 5 , October 2020 , pp. 2607 - 2619
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Copyright
Copyright © Royal Society of Edinburgh 2019

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