{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:56:21Z","timestamp":1753883781449,"version":"3.41.2"},"reference-count":20,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,5,7]],"date-time":"2012-05-07T00:00:00Z","timestamp":1336348800000},"content-version":"vor","delay-in-days":127,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100002383","name":"King Saud University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002383","id-type":"DOI","asserted-by":"publisher"}]}],"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 prove the existence of solutions for third\u2010order nonconvex state\u2010dependent sweeping process with unbounded perturbations of the form: ;, , a.e.<jats:italic>\u2009\u2009<\/jats:italic><jats:italic>\u2009\u2009<\/jats:italic><jats:italic>t<\/jats:italic> \u2208 [0, <jats:italic>T<\/jats:italic>], , , where <jats:italic>T<\/jats:italic> &gt; 0, <jats:italic>K<\/jats:italic> is a nonconvex Lipschitz set\u2010valued mapping, <jats:italic>F<\/jats:italic> is an unbounded scalarly upper semicontinuous convex set\u2010valued mapping, and <jats:italic>G<\/jats:italic> is an unbounded uniformly continuous nonconvex set\u2010valued mapping in a separable Hilbert space <jats:italic>\u210d<\/jats:italic>.<\/jats:p>","DOI":"10.1155\/2012\/695268","type":"journal-article","created":{"date-parts":[[2012,5,8]],"date-time":"2012-05-08T03:39:14Z","timestamp":1336448354000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["General Existence Results for Third\u2010Order Nonconvex State\u2010Dependent Sweeping Process with Unbounded Perturbations"],"prefix":"10.1155","volume":"2012","author":[{"given":"M.","family":"Bounkhel","sequence":"first","affiliation":[]},{"given":"B.","family":"Al-Senan","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,5,7]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(77)90085-7"},{"key":"e_1_2_7_2_2","article-title":"Existence of viable solutions for nonconvex differential inclusions","author":"Bounkhel M.","year":"2005","journal-title":"Electronic Journal of Differential Equations"},{"key":"e_1_2_7_3_2","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1515\/GMJ.2006.239","article-title":"Existence results for first and second order nonconvex sweeping processes with perturbations and with delay: fixed point approach","volume":"13","author":"Bounkhel M.","year":"2006","journal-title":"Georgian Mathematical Journal"},{"key":"e_1_2_7_4_2","first-page":"15","article-title":"Existence results for nonconvex sweeping processes with perturbations and with delay: Lipschitz case","volume":"8","author":"Bounkhel M.","year":"2002","journal-title":"Arab Journal of Mathematical Sciences"},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01027688"},{"volume-title":"Seminaire d\u2032Analyse Convexe","year":"1988","author":"Castaing C.","key":"e_1_2_7_6_2"},{"key":"e_1_2_7_7_2","series-title":"Appl. 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