An inverse problem for Sturm-Liouville equations with a fixed node

In this paper, we study a kind of inverse nodal problems for the classical Sturm-Liouville problems. To be precise, we prove the sharp lower bounds for the L1-norms of potentials when the unique node of the second eigenfunction is given. The proof is based on a strong continuity of the nodes in the...

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Bibliographic Details
Published in:	Journal of Differential Equations Vol. 454; p. 113966
Main Authors:	Chu, Jifeng, Meng, Gang, Xie, Nana
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15.02.2026
Subjects:	Measure differential equations Nodes Optimization problem Sturm-Liouville problem Measure differential equations Sturm-Liouville problem Nodes Optimization problem primary
ISSN:	0022-0396
Online Access:	Get full text
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Summary:	In this paper, we study a kind of inverse nodal problems for the classical Sturm-Liouville problems. To be precise, we prove the sharp lower bounds for the L1-norms of potentials when the unique node of the second eigenfunction is given. The proof is based on a strong continuity of the nodes in the potentials and the results on sharp bounds for the locations of the nodes. The key technique is to construct the extremal potentials.
ISSN:	0022-0396
DOI:	10.1016/j.jde.2025.113966