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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| Vydané v: | Journal of Differential Equations Ročník 454; s. 113966 |
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15.02.2026
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 113966 |
| Author | Xie, Nana Chu, Jifeng Meng, Gang |
| Author_xml | – sequence: 1 givenname: Jifeng surname: Chu fullname: Chu, Jifeng email: jifengchu@126.com organization: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China – sequence: 2 givenname: Gang surname: Meng fullname: Meng, Gang email: menggang@ucas.ac.cn organization: School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China – sequence: 3 givenname: Nana orcidid: 0009-0007-3770-668X surname: Xie fullname: Xie, Nana email: xienana1998@163.com organization: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China |
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| Cites_doi | 10.4064/sm211019-20-6 10.1016/j.jde.2018.09.039 10.1016/j.jde.2012.12.001 10.1016/j.jde.2022.01.052 10.1016/j.jde.2009.04.008 10.1007/s00605-023-01940-0 10.1002/mma.8930 10.1016/j.jde.2009.03.016 10.1016/0022-0396(88)90111-8 10.1007/s00013-019-01351-4 10.1017/prm.2024.28 10.1090/S0002-9939-2015-12304-0 10.1007/s11856-014-1097-9 10.1007/s11425-010-4081-9 10.1007/s00208-022-02556-9 10.1088/0266-5611/14/2/003 10.1007/s00208-025-03298-0 10.1007/s00009-022-02100-8 10.1088/0266-5611/22/3/010 10.1007/s00208-023-02784-7 10.1007/s10114-010-8103-x 10.1007/s00009-025-02901-7 10.1016/j.aim.2023.109272 10.1063/5.0088097 10.1016/0022-247X(89)90050-4 10.1137/S0036141096307849 10.1088/0266-5611/32/3/035007 |
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| Snippet | 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... |
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| SubjectTerms | Measure differential equations Nodes Optimization problem Sturm-Liouville problem |
| Title | An inverse problem for Sturm-Liouville equations with a fixed node |
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