{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T04:21:23Z","timestamp":1741753283634,"version":"3.38.0"},"reference-count":33,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2019,9,2]],"date-time":"2019-09-02T00:00:00Z","timestamp":1567382400000},"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":[[2019,10,3]]},"abstract":"<jats:p> In this paper, we study the following Kirchhoff type problems involving fractional p-Laplacian and critical exponents: [Formula: see text] where \u03a9 is a bounded domain in [Formula: see text] ([Formula: see text]) with Lipshcitz boundary, [Formula: see text] with [Formula: see text], [Formula: see text] is the fractional critical Sobolev exponent, \u03bb is a positive parameter, [Formula: see text] and [Formula: see text] are continuous functions, [Formula: see text] is a sign-changing function. By using the fractional version of concentration compactness principle together with mountain pass theorem, we obtained the multiplicity of solutions for the above problem. <\/jats:p>","DOI":"10.3233\/asy-191527","type":"journal-article","created":{"date-parts":[[2019,9,4]],"date-time":"2019-09-04T12:23:55Z","timestamp":1567599835000},"page":"47-61","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Fractional <i>p<\/i>-Kirchhoff problems involving critical exponents and sign-changing weight\u00a0functions"],"prefix":"10.1177","volume":"115","author":[{"given":"Sihua","family":"Liang","sequence":"first","affiliation":[{"name":"College of Mathematics, Changchun Normal University, Changchun, 130032, P.R. China. E-mail:\u00a0"}]},{"given":"Binlin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Northeast Petroleum University, Daqing, 163318, P.R. China"},{"name":"Department of Mathematics, Heilongjiang Institute of Technology, Harbin, 150050, P.R. China. E-mail:\u00a0"}]}],"member":"179","published-online":{"date-parts":[[2019,9,2]]},"reference":[{"key":"ref001","first-page":"1336","volume":"51","author":"Applebaum D.","year":"2004","journal-title":"Notices Amer. Math. Soc."},{"key":"ref002","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2013.06.016"},{"key":"ref003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1983-0699419-3"},{"key":"ref004","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-25361-4_3"},{"key":"ref005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2010.11.017"},{"key":"ref006","doi-asserted-by":"publisher","DOI":"10.1016\/j.bulsci.2011.12.004"},{"key":"ref007","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2013.08.011"},{"key":"ref008","doi-asserted-by":"publisher","DOI":"10.1007\/s11784-016-0344-6"},{"key":"ref009","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(00)00201-2"},{"key":"ref010","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2016.21.883"},{"key":"ref011","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2017.11.033"},{"key":"ref012","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2012.12.003"},{"key":"ref013","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2013.10.011"},{"key":"ref014","doi-asserted-by":"publisher","DOI":"10.1063\/1.4967976"},{"key":"ref015","doi-asserted-by":"publisher","DOI":"10.1007\/s00033-017-0805-9"},{"key":"ref016","doi-asserted-by":"publisher","DOI":"10.4171\/rmi\/6"},{"key":"ref017","doi-asserted-by":"publisher","DOI":"10.4171\/rmi\/12"},{"key":"ref018","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/29\/2\/357"},{"key":"ref019","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6544\/aaba35"},{"key":"ref020","first-page":"97","volume":"7","author":"Mishra P.K.","year":"2015","journal-title":"Adv. Pure Appl. Math."},{"key":"ref021","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-015-0891-5"},{"key":"ref022","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781316282397"},{"key":"ref023","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2016.02.012"},{"key":"ref024","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-015-0883-5"},{"key":"ref025","doi-asserted-by":"publisher","DOI":"10.1515\/anona-2015-0102"},{"key":"ref026","unstructured":"P.H.\u00a0Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Diferential Equations, CBMS Reg. Conf. Series in Math., Vol.\u00a065, 1984."},{"key":"ref027","doi-asserted-by":"publisher","DOI":"10.1080\/03605302.2014.918144"},{"key":"ref028","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-2014-05884-4"},{"key":"ref029","doi-asserted-by":"publisher","DOI":"10.1007\/s13163-015-0170-1"},{"key":"ref030","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2014.11.055"},{"key":"ref031","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2015.0034"},{"key":"ref032","doi-asserted-by":"publisher","DOI":"10.1515\/ans-2016-6002"},{"key":"ref033","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(92)90210-6"}],"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-191527","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/ASY-191527","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-191527","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T06:15:02Z","timestamp":1741673702000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-191527"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,2]]},"references-count":33,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2019,10,3]]}},"alternative-id":["10.3233\/ASY-191527"],"URL":"https:\/\/doi.org\/10.3233\/asy-191527","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"type":"print","value":"0921-7134"},{"type":"electronic","value":"1875-8576"}],"subject":[],"published":{"date-parts":[[2019,9,2]]}}}