{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:14:25Z","timestamp":1753881265386,"version":"3.41.2"},"reference-count":28,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,6,3]],"date-time":"2012-06-03T00:00:00Z","timestamp":1338681600000},"content-version":"vor","delay-in-days":154,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>We study the following fourth\u2010order elliptic equations: \u0394<jats:sup>2<\/jats:sup><jats:italic>u<\/jats:italic> + <jats:italic>a<\/jats:italic>\u0394<jats:italic>u<\/jats:italic> = <jats:italic>f<\/jats:italic>(<jats:italic>x<\/jats:italic>, <jats:italic>u<\/jats:italic>), <jats:italic>\u2009\u2009<\/jats:italic><jats:italic>x<\/jats:italic> \u2208 \u03a9, <jats:italic>\u2009\u2009<\/jats:italic><jats:italic>u<\/jats:italic> = \u0394<jats:italic>u<\/jats:italic> = 0, <jats:italic>\u2009<\/jats:italic><jats:italic>x<\/jats:italic> \u2208 <jats:italic>\u2202<\/jats:italic>\u03a9, where \u03a9 \u2282 <jats:italic>\u211d<\/jats:italic><jats:sup><jats:italic>N<\/jats:italic><\/jats:sup> is a bounded domain with smooth boundary <jats:italic>\u2202<\/jats:italic>\u03a9 and <jats:italic>f<\/jats:italic>(<jats:italic>x<\/jats:italic>, <jats:italic>u<\/jats:italic>) is asymptotically linear with respect to <jats:italic>u<\/jats:italic> at infinity. Using an equivalent version of Cerami\u2032s condition and the symmetric mountain pass lemma, we obtain the existence of multiple solutions for the equations.<\/jats:p>","DOI":"10.1155\/2012\/749059","type":"journal-article","created":{"date-parts":[[2012,6,4]],"date-time":"2012-06-04T15:32:15Z","timestamp":1338823935000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Multiplicity of Solutions for a Class of Fourth\u2010Order Elliptic Problems with Asymptotically Linear Term"],"prefix":"10.1155","volume":"2012","author":[{"given":"Qiong","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dengfeng","family":"L\u00fc","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2012,6,3]]},"reference":[{"key":"e_1_2_5_1_2","doi-asserted-by":"publisher","DOI":"10.1137\/1032120"},{"key":"e_1_2_5_2_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1994.1049"},{"key":"e_1_2_5_3_2","first-page":"1","article-title":"Radial solutions of singular nonlinear biharmonic equations and applications to conformal geometry","volume":"37","author":"McKenna P. 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