{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:52:14Z","timestamp":1777449134519,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2014,8,1]],"date-time":"2014-08-01T00:00:00Z","timestamp":1406851200000},"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":[[2014,8]]},"abstract":"<jats:p>\n                    Let \u03a9\u2282R\n                    <jats:sup>N<\/jats:sup>\n                    (N\u22652) be a bounded C\n                    <jats:sup>2<\/jats:sup>\n                    domain containing 0, 0&lt;\u03b1&lt;1 and 0&lt;p&lt;N\/(N\u22122\u03b1). If \u03b4\n                    <jats:sub>0<\/jats:sub>\n                    is the Dirac mass at 0 and k&gt;0, we prove that the weakly singular solution u\n                    <jats:sub>k<\/jats:sub>\n                    of (E\n                    <jats:sub>k<\/jats:sub>\n                    ) (\u2212\u0394)\n                    <jats:sup>\u03b1<\/jats:sup>\n                    u+u\n                    <jats:sup>p<\/jats:sup>\n                    =k\u03b4\n                    <jats:sub>0<\/jats:sub>\n                    in \u03a9, which vanishes in \u03a9\n                    <jats:sup>c<\/jats:sup>\n                    , is a classical solution of (E\n                    <jats:sub>*<\/jats:sub>\n                    ) (\u2212\u0394)\n                    <jats:sup>\u03b1<\/jats:sup>\n                    u+u\n                    <jats:sup>p<\/jats:sup>\n                    =0 in \u03a9\\{0} with the same outer data. Let A=[N\/2\u03b1,1+2\u03b1\/N) for N=2,3 and (\u221a5\u22121)\/4N&lt;\u03b1&lt;1, otherwise, A=\u2205; we derive that u\n                    <jats:sub>k<\/jats:sub>\n                    converges to \u221e in whole \u03a9 as k\u2192\u221e for p\u2208(0,1+2\u03b1\/N)\\A, while the limit of u\n                    <jats:sub>k<\/jats:sub>\n                    is a strongly singular solution of (E\n                    <jats:sub>*<\/jats:sub>\n                    ) for 1+2\u03b1\/N&lt;p&lt;N\/(N\u22122\u03b1).\n                  <\/jats:p>","DOI":"10.3233\/asy-141216","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:33:28Z","timestamp":1575056008000},"page":"165-184","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":13,"title":["Weakly and strongly singular solutions of semilinear fractional elliptic equations"],"prefix":"10.1177","volume":"88","author":[{"given":"Huyuan","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Jiangxi Normal University, Nanchang, China"},{"name":"Departamento de Ingenier\u00eda Matem\u00e1tica, Universidad de Chile, Santiago, Chile. E-mail: chenhuyuan@yeah.net"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Laurent","family":"V\u00e9ron","sequence":"additional","affiliation":[{"name":"Laboratoire de Math\u00e9matiques et Physique Th\u00e9orique, Universit\u00e9 Fran\u00e7ois Rabelais, Tours, France. E-mail: Laurent.Veron@lmpt.univ-tours.fr"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2014,8,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-141216","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-141216","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:08Z","timestamp":1777380008000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-141216"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,8]]}},"alternative-id":["10.3233\/ASY-141216"],"URL":"https:\/\/doi.org\/10.3233\/asy-141216","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,8]]}}}