{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:58:33Z","timestamp":1760234313263,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,5,7]],"date-time":"2021-05-07T00:00:00Z","timestamp":1620345600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771253, 12071254"],"award-info":[{"award-number":["11771253, 12071254"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The present paper is concerned with the spectral theory of nonlocal Sturm\u2013Liouville eigenvalue problems on a finite interval. The continuity, differentiability and comparison results of eigenvalues with respect to the nonlocal potentials are studied, and the oscillation properties of eigenfunctions are investigated. The comparison result of eigenvalues and the oscillation properties of eigenfunctions indicate that the spectral properties of nonlocal problems are very different from those of classical Sturm\u2013Liouville problems. Some examples are given to explain this essential difference.<\/jats:p>","DOI":"10.3390\/sym13050820","type":"journal-article","created":{"date-parts":[[2021,5,7]],"date-time":"2021-05-07T22:36:24Z","timestamp":1620426984000},"page":"820","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Properties of Eigenvalues and Eigenfunctions for Nonlocal Sturm\u2013Liouville Problems"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1542-3917","authenticated-orcid":false,"given":"Zhiwen","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shandong University at Weihai, Weihai 264209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0716-8351","authenticated-orcid":false,"given":"Jiangang","family":"Qi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shandong University at Weihai, Weihai 264209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1088\/0266-5611\/23\/2\/005","article-title":"Inverse spectral problems for nonlocal Sturm\u2013Liouville operators","volume":"23","author":"Albeverio","year":"2007","journal-title":"Inverse Probl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"884","DOI":"10.1016\/j.jmaa.2006.10.070","article-title":"Schr\u00f6dinger operators with nonlocal point interactions","volume":"332","author":"Albeverio","year":"2007","journal-title":"J. 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Inverse Spectral Theory, Academic Press."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/5\/820\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:57:58Z","timestamp":1760162278000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/5\/820"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,7]]},"references-count":14,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2021,5]]}},"alternative-id":["sym13050820"],"URL":"https:\/\/doi.org\/10.3390\/sym13050820","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,5,7]]}}}