{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:48:22Z","timestamp":1777448902016,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2011,8,1]],"date-time":"2011-08-01T00:00:00Z","timestamp":1312156800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2011,8]]},"abstract":"<jats:p>We consider a boundary value problem generated by Sturm\u2013Liouville equations on the edges of a star-shaped graph. Thereby a continuity condition and a condition depending on the spectral parameter is imposed at the interior vertex, corresponding to the case of damping in the problem of small transversal vibrations of a star graph of smooth inhomogeneous strings. At the pendant vertices Dirichlet boundary conditions are imposed. We describe the eigenvalue asymptotics of the problem under consideration.<\/jats:p>","DOI":"10.3233\/asy-2011-1040","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:17:09Z","timestamp":1575055029000},"page":"169-185","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Eigenvalue asymptotics for a star-graph damped vibrations problem"],"prefix":"10.1177","volume":"73","author":[{"given":"Vyacheslav","family":"Pivovarchik","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics and Informatics, South-Ukrainian State Pedagogical University, Staroportofrankovskaya str. 26, UA-65020 Odessa, Ukraine. E-mail: v.pivovarchik@paco.net, vnp@dtp.odessa.ua"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Harald","family":"Woracek","sequence":"additional","affiliation":[{"name":"Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8\u201310\/101, A-1040 Vienna, Austria. E-mail: harald.woracek@tuwien.ac.at"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2011,8,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2011-1040","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2011-1040","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:20Z","timestamp":1777379960000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2011-1040"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,8]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,8]]}},"alternative-id":["10.3233\/ASY-2011-1040"],"URL":"https:\/\/doi.org\/10.3233\/asy-2011-1040","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,8]]}}}