{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:48:46Z","timestamp":1777448926333,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2012,3,1]],"date-time":"2012-03-01T00:00:00Z","timestamp":1330560000000},"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":[[2012,3]]},"abstract":"<jats:p>\n                    We consider the positive solutions u of \u2212\u0394u+u\u2212u\n                    <jats:sup>p<\/jats:sup>\n                    =0 in [0,2\u03c0]\u00d7R\n                    <jats:sup>N\u22121<\/jats:sup>\n                    , which are 2\u03c0-periodic in x\n                    <jats:sub>1<\/jats:sub>\n                    and tend uniformly to 0 in the other variables. There exists a constant C such that any solution u verifies u(x\n                    <jats:sub>1<\/jats:sub>\n                    ,x\u2032)\u2264Cw\n                    <jats:sub>0<\/jats:sub>\n                    (x\u2032) where w\n                    <jats:sub>0<\/jats:sub>\n                    is the ground state solution of \u2212\u0394v+v\u2212v\n                    <jats:sup>p<\/jats:sup>\n                    =0 in R\n                    <jats:sup>N\u22121<\/jats:sup>\n                    . We prove that exactly the same estimate is true when the period is 2\u03c0\/\u03b5, even when \u03b5 tends to 0. We have a similar result for the gradient.\n                  <\/jats:p>","DOI":"10.3233\/asy-2011-1076","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:19:53Z","timestamp":1575055193000},"page":"115-122","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["An a priori estimate for the singly periodic solutions of a semilinear equation"],"prefix":"10.1177","volume":"76","author":[{"given":"Genevi\u00e8ve","family":"Allain","sequence":"first","affiliation":[{"name":"Laboratoire d'Analyse et de Math\u00e9matiques Appliqu\u00e9es, Facult\u00e9 de Sciences et Technologie, Universit\u00e9 Paris-Est Cr\u00e9teil, Cr\u00e9teil, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anne","family":"Beaulieu","sequence":"additional","affiliation":[{"name":"Laboratoire d'Analyse et de Math\u00e9matiques Appliqu\u00e9es, Universit\u00e9 Paris-Est Marne la Vall\u00e9e, Marne la Vall\u00e9e, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2012,3,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2011-1076","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2011-1076","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:27Z","timestamp":1777379967000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2011-1076"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,3]]}},"alternative-id":["10.3233\/ASY-2011-1076"],"URL":"https:\/\/doi.org\/10.3233\/asy-2011-1076","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3]]}}}