{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:54:46Z","timestamp":1777449286777,"version":"3.51.4"},"reference-count":19,"publisher":"SAGE Publications","issue":"1-2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ASY"],"published-print":{"date-parts":[[2015,10,15]]},"DOI":"10.3233\/asy-151324","type":"journal-article","created":{"date-parts":[[2015,10,20]],"date-time":"2015-10-20T10:53:45Z","timestamp":1445338425000},"page":"79-100","source":"Crossref","is-referenced-by-count":2,"title":["Nonlocal problems at critical growth in contractible domains"],"prefix":"10.1177","volume":"95","author":[{"given":"Sunra","family":"Mosconi","sequence":"first","affiliation":[{"name":"Dipartimento di Informatica, Universit\u00e0 degli Studi di Verona, Verona, Italy. E-mails:\u00a0sunra.mosconi@univr.it,\u00a0marco.squassina@univr.it"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naoki","family":"Shioji","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Engineering, Yokohama National University, Yokohama, Japan. E-mail:\u00a0shioji@ynu.ac.jp"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Squassina","sequence":"additional","affiliation":[{"name":"Dipartimento di Informatica, Universit\u00e0 degli Studi di Verona, Verona, Italy. E-mails:\u00a0sunra.mosconi@univr.it,\u00a0marco.squassina@univr.it"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"key":"10.3233\/ASY-151324_ref1","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1002\/cpa.3160410302","article-title":"On a nonlinear elliptic equation involving the critical Sobolev exponent: The effect of the topology of the domain","volume":"41","author":"Bahri","year":"1988","journal-title":"Comm. Pure Appl. Math."},{"key":"10.3233\/ASY-151324_ref2","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.1080\/03605300600987306","article-title":"An extension problem related to the fractional Laplacian","volume":"32","author":"Caffarelli","year":"2007","journal-title":"Comm. Partial Differential Equations"},{"key":"10.3233\/ASY-151324_ref3","doi-asserted-by":"crossref","unstructured":"[3]K.-C.\u00a0Chang, Infinite-Dimensional Morse Theory and Multiple Solution Problems, Progress in Nonlinear Differential Equations and Their Applications, Vol.\u00a06, Birkh\u00e4user, Boston, 1993.","DOI":"10.1007\/978-1-4612-0385-8"},{"key":"10.3233\/ASY-151324_ref4","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1002\/cpa.20116","article-title":"Classification of solutions for an integral equation","volume":"59","author":"Chen","year":"2006","journal-title":"Comm. Pure Appl. Math."},{"key":"10.3233\/ASY-151324_ref5","first-page":"209","article-title":"Topologie et cas limite del injections de Sobolev","volume":"299","author":"Coron","year":"1984","journal-title":"C.R. Acad. Sc. Paris"},{"key":"10.3233\/ASY-151324_ref6","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.jmaa.2004.03.034","article-title":"Best constants for Sobolev inequalities for higher order fractional derivatives","volume":"295","author":"Cotsiolis","year":"2004","journal-title":"J. Math. Anal. Appl."},{"key":"10.3233\/ASY-151324_ref7","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1112\/blms\/20.6.600","article-title":"A note on an equation with critical exponent","volume":"20","author":"Dancer","year":"1988","journal-title":"Bull. Lond. Math. Soc."},{"key":"10.3233\/ASY-151324_ref8","first-page":"83","article-title":"Positive solutions of \u2212 \u0394 u + u ( n + 2 ) \/ ( n \u2212 2 ) = 0 on contractible domains","volume":"2","author":"Ding","year":"1989","journal-title":"J. Partial Differential Equations"},{"key":"10.3233\/ASY-151324_ref9","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1016\/0022-247X(74)90025-0","article-title":"On the variational principle","volume":"47","author":"Ekeland","year":"1974","journal-title":"J. Math. Anal. Appl."},{"key":"10.3233\/ASY-151324_ref10","doi-asserted-by":"crossref","first-page":"2205","DOI":"10.1016\/j.jfa.2012.06.018","article-title":"Nonexistence results for a class of fractional elliptic boundary value problems","volume":"263","author":"Fall","year":"2012","journal-title":"J. Funct. Anal."},{"key":"10.3233\/ASY-151324_ref11","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/s00030-014-0292-z","article-title":"H s versus C 0 -weighted minimizers","volume":"22","author":"Iannizzotto","year":"2015","journal-title":"NoDEA"},{"key":"10.3233\/ASY-151324_ref13","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1007\/s00526-013-0656-y","article-title":"Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces","volume":"50","author":"Palatucci","year":"2014","journal-title":"Calculus of Variations and PDEs"},{"key":"10.3233\/ASY-151324_ref14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.na.2014.12.027","article-title":"A global compactness type result for Palais\u2013Smale sequences in fractional Sobolev spaces","volume":"117","author":"Palatucci","year":"2015","journal-title":"Nonlinear Anal."},{"key":"10.3233\/ASY-151324_ref15","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/BF01168296","article-title":"Multiplicity of positive solutions of nonlinear elliptic equations with critical Sobolev exponent in some contractible domains","volume":"65","author":"Passaseo","year":"1989","journal-title":"Manuscripta Math."},{"key":"10.3233\/ASY-151324_ref16","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1007\/s00205-014-0740-2","article-title":"The Poh\u01d2zaev identity for the fractional Laplacian","volume":"213","author":"Ros-Oton","year":"2014","journal-title":"Arch. Ration. Mech. Anal."},{"key":"10.3233\/ASY-151324_ref17","doi-asserted-by":"crossref","first-page":"103","DOI":"10.57262\/die\/1418310423","article-title":"Coron problem for fractional equations","volume":"28","author":"Secchi","year":"2015","journal-title":"Differential Integral Equations"},{"key":"10.3233\/ASY-151324_ref18","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1090\/S0002-9947-2014-05884-4","article-title":"The Brezis\u2013Nirenberg result for the fractional Laplacian","volume":"367","author":"Servadei","year":"2015","journal-title":"Trans. Amer. Math. Soc."},{"key":"10.3233\/ASY-151324_ref19","unstructured":"[19]E.M.\u00a0Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, Vol.\u00a030, Princeton Univ. Press, Princeton, NJ, 1970."},{"key":"10.3233\/ASY-151324_ref20","doi-asserted-by":"crossref","unstructured":"[20]W.P.\u00a0Ziemer, Weakly Differentiable Functions, Graduate Texts in Mathematics, Vol.\u00a0120, Springer, New York, 1989.","DOI":"10.1007\/978-1-4612-1015-3"}],"container-title":["Asymptotic Analysis"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/ASY-151324","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:40Z","timestamp":1777380040000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/ASY-151324"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,15]]},"references-count":19,"journal-issue":{"issue":"1-2"},"URL":"https:\/\/doi.org\/10.3233\/asy-151324","relation":{},"ISSN":["1875-8576","0921-7134"],"issn-type":[{"value":"1875-8576","type":"electronic"},{"value":"0921-7134","type":"print"}],"subject":[],"published":{"date-parts":[[2015,10,15]]}}}