{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:52:33Z","timestamp":1777449153857,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2014,9,1]],"date-time":"2014-09-01T00:00:00Z","timestamp":1409529600000},"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":[[2014,9]]},"abstract":"<jats:p>This paper is concerned with the multiplicity of nontrivial solutions in an Orlicz\u2013Sobolev space for a nonlocal problem with critical growth, involving N-functions and theory of locally Lipschitz continuous functionals. More precisely, in this paper, we study a result of multiplicity to the following multivalued elliptic problem:<\/jats:p>\n                  <jats:p>\n                    \u2212M(\u222b\n                    <jats:sub>\u03a9<\/jats:sub>\n                    \u03a6(|\u2207u|)\u2009dx)\u0394\n                    <jats:sub>\u03a6<\/jats:sub>\n                    u\u2208\u2202F(\u00b7,u)+\u03b1h(u) \u2003 in \u03a9,\n                  <\/jats:p>\n                  <jats:p>\n                    u\u2208W\n                    <jats:sub>0<\/jats:sub>\n                    <jats:sup>1<\/jats:sup>\n                    L\n                    <jats:sub>\u03a6<\/jats:sub>\n                    (\u03a9),\n                  <\/jats:p>\n                  <jats:p>\n                    where \u03a9\u2282R\n                    <jats:sup>N<\/jats:sup>\n                    is a bounded smooth domain, N\u22653, M is a continuous function, \u03a6 is an N-function, h is an odd increasing homeomorphism from R to R, \u03b1 is positive parameter, \u0394\n                    <jats:sub>\u03a6<\/jats:sub>\n                    is the corresponding \u03a6-Laplacian and \u2202F(\u00b7,t) stands for Clarke generalized of a function F linked with critical growth. We use genus theory to obtain the main result.\n                  <\/jats:p>","DOI":"10.3233\/asy-141243","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:34:47Z","timestamp":1575056087000},"page":"151-172","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["On a \u03a6-Kirchhoff multivalued problem with critical growth in an Orlicz\u2013Sobolev space"],"prefix":"10.1177","volume":"89","author":[{"given":"Giovany M.","family":"Figueiredo","sequence":"first","affiliation":[{"name":"Universidade Federal do Par\u00e1, Faculdade de Matem\u00e1tica, 66075-110, Bel\u00e9m, PA, Brazil. E-mail: giovany@ufpa.br"}]},{"given":"Jefferson A.","family":"Santos","sequence":"additional","affiliation":[{"name":"Universidade Federal de Campina Grande, Unidade Acad\u00eamica de Matem\u00e1tica e Estat\u00edstica, 58109-970, Campina Grande, PB, Brazil. E-mail: jefferson@dme.ufcg.edu.br"}]}],"member":"179","published-online":{"date-parts":[[2014,9,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-141243","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-141243","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:11Z","timestamp":1777380011000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-141243"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2014,9]]}},"alternative-id":["10.3233\/ASY-141243"],"URL":"https:\/\/doi.org\/10.3233\/asy-141243","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,9]]}}}