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Optimal inverse problems of potentials for two given eigenvalues of Sturm–Liouville problems

Part of: Boundary value problems Ordinary differential operators

Published online by Cambridge University Press:  07 March 2024

Min Zhao  and
Jiangang Qi
Min Zhao
Affiliation:
Department of Mathematics, Shandong University at Weihai, Weihai 264209, P. R. China (zhaomin215@mail.sdu.edu.cn; qijiangang@sdu.edu.cn)
Jiangang Qi
Affiliation:
Department of Mathematics, Shandong University at Weihai, Weihai 264209, P. R. China (zhaomin215@mail.sdu.edu.cn; qijiangang@sdu.edu.cn)
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Abstract

The present paper is concerned with the infimum of the norm of potentials for Sturm–Liouville eigenvalue problems with Dirichlet boundary condition such that the first two eigenvalues are known. The explicit quantity of the infimum is given by the two eigenvalues.

Keywords

optimal inverse problemLyapunov inequalitymin-max principleSturm–Liouville problemeigenvalue

MSC classification

Primary: 34B20: Weyl theory and its generalizations
Secondary: 34L99: None of the above, but in this section 34L05: General spectral theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 24
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Copyright
Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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