{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T19:28:46Z","timestamp":1648582126473},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"1-2","license":[{"start":{"date-parts":[[2011,11,14]],"date-time":"2011-11-14T00:00:00Z","timestamp":1321228800000},"content-version":"unspecified","delay-in-days":8352,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"published-print":{"date-parts":[[1989]]},"abstract":"<jats:title>Synopsis<\/jats:title><jats:p>We consider the nonlinear elliptic problem at resonance, \u0394<jats:italic>u<\/jats:italic> + \u03bb<jats:sub>1<\/jats:sub><jats:italic>u<\/jats:italic> + <jats:italic>f<\/jats:italic>(<jats:italic>x, u<\/jats:italic>) = <jats:italic>h<\/jats:italic>(<jats:italic>x<\/jats:italic>) in \u03a9, <jats:italic>u<\/jats:italic> = 0 on \u2202\u03a9, where <jats:italic>\u03a9<\/jats:italic> is a bounded smooth domain in \u211d<jats:sup><jats:italic>N<\/jats:italic><\/jats:sup>, \u03bb<jats:sub>l<\/jats:sub> is the first eigenvalue of \u2013\u0394 in \u03a9 and <jats:italic>h(x)<\/jats:italic> is orthogonal to the first eigenfunction. We give some conditions of solvability in terms of the primitive of <jats:italic>f<\/jats:italic> with respect to <jats:italic>u<\/jats:italic>.<\/jats:p>","DOI":"10.1017\/s0308210500028237","type":"journal-article","created":{"date-parts":[[2011,11,14]],"date-time":"2011-11-14T13:17:50Z","timestamp":1321276670000},"page":"177-185","source":"Crossref","is-referenced-by-count":6,"title":["Vanational elliptic problems involving noncoercive functionals"],"prefix":"10.1017","volume":"112","author":[{"given":"Miguel","family":"Ramos","sequence":"first","affiliation":[]},{"given":"Luis","family":"Sanchez","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2011,11,14]]},"reference":[{"key":"S0308210500028237_ref019","doi-asserted-by":"publisher","DOI":"10.1080\/00036818708839691"},{"key":"S0308210500028237_ref018","doi-asserted-by":"publisher","DOI":"10.1090\/cbms\/065"},{"key":"S0308210500028237_ref016","doi-asserted-by":"publisher","DOI":"10.1016\/S0294-1449(16)30376-6"},{"key":"S0308210500028237_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/BF00251362"},{"key":"S0308210500028237_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(85)90093-9"},{"key":"S0308210500028237_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(87)90121-5"},{"key":"S0308210500028237_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(79)90091-9"},{"key":"S0308210500028237_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(88)90266-1"},{"key":"S0308210500028237_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(87)90134-3"},{"key":"S0308210500028237_ref004","doi-asserted-by":"publisher","DOI":"10.1080\/03605308108820172"},{"key":"S0308210500028237_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF01773936"},{"key":"S0308210500028237_ref002","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1976.25.25074"},{"key":"S0308210500028237_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(86)90042-8"},{"key":"S0308210500028237_ref011","unstructured":"11. Iannacci R. , Nkashama M. N. and Ward J. R. , Jr. Nonlinear Second Order Elliptic Partial Differential Equations at Resonance (Memphis State University Report Series 87\u201312)."},{"key":"S0308210500028237_ref013","first-page":"49","volume-title":"Equadiff 6, Brno","author":"Mawhin","year":"1985"},{"key":"S0308210500028237_ref007","unstructured":"7. de D. G. Figueiredo and Gossez J. P. . Nonresonance below the first eigenvalue for a semilinear elliptic problem (to appear)."},{"key":"S0308210500028237_ref014","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1985-0776200-X"},{"key":"S0308210500028237_ref005","first-page":"225","article-title":"Characterization of the ranges of some nonlinear operators and application to boundary value problems","volume":"5","author":"Brezis","year":"1978","journal-title":"Ann. Scuola Norm. Sup. Pisa Cl. Sci"},{"key":"S0308210500028237_ref017","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2061-7"}],"container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0308210500028237","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,19]],"date-time":"2019-05-19T21:23:06Z","timestamp":1558300986000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0308210500028237\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989]]},"references-count":19,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[1989]]}},"alternative-id":["S0308210500028237"],"URL":"https:\/\/doi.org\/10.1017\/s0308210500028237","relation":{},"ISSN":["0308-2105","1473-7124"],"issn-type":[{"value":"0308-2105","type":"print"},{"value":"1473-7124","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989]]}}}