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Estimates on the non-real eigenvalues of regular indefinite Sturm–Liouville problems

Published online by Cambridge University Press:  01 December 2014

Jussi Behrndt
Affiliation:
Institut für Numerische Mathematik, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria, (behrndt@tugraz.at)
Shaozhu Chen
Affiliation:
Department of Mathematics, Shandong University (Weihai), Weihai 264209, People's Republic of China, (szchen@sdu.edu.cn)
Friedrich Philipp
Affiliation:
Institut für Mathematik, Technische Universität Clausthal, Erzstraße 1, 38678 Clausthal–Zellerfeld, Germany, (fmphilipp@gmail.com)
Jiangang Qi
Affiliation:
Department of Mathematics, Shandong University (Weihai), Weihai 264209, People's Republic of China, (qjg816@163.com)

Abstract

Regular Sturm–Liouville problems with indefinite weight functions may possess finitely many non-real eigenvalues. In this paper we prove explicit bounds on the real and imaginary parts of these eigenvalues in terms of the coefficients of the differential expression.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2014 

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