{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:27:45Z","timestamp":1760239665885,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,12,2]],"date-time":"2020-12-02T00:00:00Z","timestamp":1606867200000},"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":["62073202","11671237"],"award-info":[{"award-number":["62073202","11671237"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"a project of Shandong Province Higher Educational Science and Technology Program of China","award":["J18KA233"],"award-info":[{"award-number":["J18KA233"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper is concerned with multiple solutions for a class of nonlinear fourth-order boundary value problems with parameters. By constructing a special cone and applying fixed point index theory, the multiple solutions for the considered systems are obtained under some suitable assumptions. The main feature of obtained solutions (u(t),v(t)) is that the solution u(t) is positive, and the other solution v(t) may change sign. Finally, two examples with continuous function f1 being positive and f2 being semipositone are worked out to illustrate the main results.<\/jats:p>","DOI":"10.3390\/sym12121989","type":"journal-article","created":{"date-parts":[[2020,12,2]],"date-time":"2020-12-02T07:49:54Z","timestamp":1606895394000},"page":"1989","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Multiple Solutions for a Class of Nonlinear Fourth-Order Boundary Value Problems"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2944-5719","authenticated-orcid":false,"given":"Longfei","family":"Lin","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4911-9016","authenticated-orcid":false,"given":"Yansheng","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0817-6014","authenticated-orcid":false,"given":"Daliang","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1016\/j.jmaa.2005.07.057","article-title":"Eigenvalue comparisons for boundary value problems for second order difference equations","volume":"320","author":"Ji","year":"2006","journal-title":"J. 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