{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:49:03Z","timestamp":1777448943977,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2012,8,1]],"date-time":"2012-08-01T00:00:00Z","timestamp":1343779200000},"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":[[2012,8]]},"abstract":"<jats:p>In this article we study existence of boundary blow up solutions for some fractional elliptic equations including<\/jats:p>\n                  <jats:p>\n                    (\u2212\u0394)\n                    <jats:sup>\u03b1<\/jats:sup>\n                    u+u\n                    <jats:sup>p<\/jats:sup>\n                    =f\u2003in \u03a9,\n                  <\/jats:p>\n                  <jats:p>\n                    u=g\u2003on \u03a9\n                    <jats:sup>c<\/jats:sup>\n                    ,\n                  <\/jats:p>\n                  <jats:p>\n                    lim\u2009\n                    <jats:sub>x\u2208\u03a9,x\u2192\u2202\u03a9<\/jats:sub>\n                    u(x)=\u221e,\n                  <\/jats:p>\n                  <jats:p>\n                    where \u03a9 is a bounded domain of class C\n                    <jats:sup>2<\/jats:sup>\n                    , \u03b1\u2208(0,1) and the functions f\u2009:\u03a9\u2192R and g\u2009:R\n                    <jats:sup>N<\/jats:sup>\n                    \\\u03a9\n                    <jats:sup>\u2212<\/jats:sup>\n                    \u2192R are continuous. We obtain existence of a solution u when the boundary value g blows up at the boundary and we get explosion rate for u under an additional assumption on the rate of explosion of g. Our results are extended for an ample class of elliptic fractional nonlinear operators of Isaacs type.\n                  <\/jats:p>","DOI":"10.3233\/asy-2011-1081","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:21:36Z","timestamp":1575055296000},"page":"123-144","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":21,"title":["Boundary blow up solutions for fractional elliptic equations"],"prefix":"10.1177","volume":"78","author":[{"given":"Patricio","family":"Felmer","sequence":"first","affiliation":[{"name":"Departamento de Ingenier\u00eda Matem\u00e1tica and Centro de Modelamiento Matem\u00e1tico, Universidad de Chile, Santiago, Chile. E-mail: pfelmer@dim.uchile.cl"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Quaas","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidad T\u00e9cnica Fedrico Santa Mar\u00eda, Valpara\u00edso, Chile. E-mail: alexander.quaas@usm.cl"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2012,8,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2011-1081","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2011-1081","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:31Z","timestamp":1777379971000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2011-1081"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,8]]}},"alternative-id":["10.3233\/ASY-2011-1081"],"URL":"https:\/\/doi.org\/10.3233\/asy-2011-1081","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,8]]}}}