Abstract
A node of a Sturm–Liouville problem is an interior zero of an eigenfunction. The aim of this paper is to present a simple and new proof of the result on sharp bounds of the node for the Sturm–Liouville equation with the Dirichlet boundary condition when the \(L^1\) norm of potentials is given. Based on the outer approximation method, we will reduce this infinite-dimensional optimization problem to the finite-dimensional optimization problem.
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Acknowledgements
The first author is supported by The Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No.18KJB110007). The second author is supported by the National Natural Science Foundation of China (Grant No. 12071456 and 12271509) and the Fundamental Research Funds for the Central Universities. The fourth author is supported by the National Natural Science Foundation of China (Grant No. 12001299).
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Communicated by Adrian Constantin.
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Feng, H., Meng, G., Yan, P. et al. Sharp bounds of nodes for Sturm–Liouville equations. Monatsh Math (2024). https://doi.org/10.1007/s00605-023-01940-0
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DOI: https://doi.org/10.1007/s00605-023-01940-0