{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:44Z","timestamp":1740134564181,"version":"3.37.3"},"reference-count":29,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11161041","31260098","zyz2012074"],"award-info":[{"award-number":["11161041","31260098","zyz2012074"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11161041","31260098","zyz2012074"],"award-info":[{"award-number":["11161041","31260098","zyz2012074"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["11161041","31260098","zyz2012074"],"award-info":[{"award-number":["11161041","31260098","zyz2012074"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"We are concerned with the following modified nonlinear Schr\u00f6dinger system:-<\/mml:mo>\u0394<\/mml:mi>u<\/mml:mi><\/mml:math>+<\/mml:mo>u<\/mml:mi>-<\/mml:mo>(<\/mml:mo>1<\/mml:mn>\/<\/mml:mo>2<\/mml:mn>)<\/mml:mo>u<\/mml:mi>\u0394<\/mml:mi>(<\/mml:mo>u<\/mml:mi><\/mml:mrow>2<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow>)<\/mml:mo><\/mml:mrow>=<\/mml:mo>(<\/mml:mo>2<\/mml:mn>\u03b1<\/mml:mi>\/<\/mml:mo>(<\/mml:mo>\u03b1<\/mml:mi>+<\/mml:mo>\u03b2<\/mml:mi>)<\/mml:mo>)<\/mml:mo>|<\/mml:mo>u<\/mml:mi>|<\/mml:mo><\/mml:mrow>\u03b1<\/mml:mi>-<\/mml:mo>2<\/mml:mn><\/mml:mrow><\/mml:msup>|<\/mml:mo>v<\/mml:mi>|<\/mml:mo><\/mml:mrow>\u03b2<\/mml:mi><\/mml:mrow><\/mml:msup>u<\/mml:mi><\/mml:math>,\u2009\u2009x<\/mml:mi>\u2208<\/mml:mo>\u03a9<\/mml:mi><\/mml:math>,\u2009\u2009-<\/mml:mo>\u0394<\/mml:mi>v<\/mml:mi>+<\/mml:mo>v<\/mml:mi>-<\/mml:mo>(<\/mml:mo>1<\/mml:mn>\/<\/mml:mo>2<\/mml:mn>)<\/mml:mo>v<\/mml:mi>\u0394<\/mml:mi>(<\/mml:mo>v<\/mml:mi><\/mml:mrow>2<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow>)<\/mml:mo><\/mml:mrow>=<\/mml:mo>(<\/mml:mo>2<\/mml:mn>\u03b2<\/mml:mi>\/<\/mml:mo>(<\/mml:mo>\u03b1<\/mml:mi>+<\/mml:mo>\u03b2<\/mml:mi>)<\/mml:mo>)<\/mml:mo>|<\/mml:mo>u<\/mml:mi>|<\/mml:mo><\/mml:mrow>\u03b1<\/mml:mi><\/mml:mrow><\/mml:msup>|<\/mml:mo>v<\/mml:mi>|<\/mml:mo><\/mml:mrow>\u03b2<\/mml:mi>-<\/mml:mo>2<\/mml:mn><\/mml:mrow><\/mml:msup>v<\/mml:mi><\/mml:math>,\u2009\u2009x<\/mml:mi>\u2208<\/mml:mo>\u03a9<\/mml:mi><\/mml:math>,\u2009\u2009u<\/mml:mi>=<\/mml:mo>0<\/mml:mn><\/mml:math>,\u2009\u2009v<\/mml:mi>=<\/mml:mo>0<\/mml:mn><\/mml:math>,\u2009\u2009x<\/mml:mi>\u2208<\/mml:mo>\u2202<\/mml:mo>\u03a9<\/mml:mi><\/mml:math>, where\u03b1<\/mml:mi>><\/mml:mo>2<\/mml:mn><\/mml:math>,\u2009\u2009\u03b2<\/mml:mi>><\/mml:mo>2<\/mml:mn><\/mml:math>,\u2009\u2009\u03b1<\/mml:mi>+<\/mml:mo>\u03b2<\/mml:mi><<\/mml:mo>2<\/mml:mn>\u00b7<\/mml:mo>2<\/mml:mn><\/mml:mrow>*<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:math>,\u2009\u20092<\/mml:mn><\/mml:mrow>*<\/mml:mi><\/mml:mrow><\/mml:msup>=<\/mml:mo>2<\/mml:mn>N<\/mml:mi>\/<\/mml:mo>(<\/mml:mo>N<\/mml:mi>-<\/mml:mo>2<\/mml:mn>)<\/mml:mo><\/mml:math>is the critical Sobolev exponent, and\u03a9<\/mml:mi>\u2282<\/mml:mo>\u211d<\/mml:mi><\/mml:mrow>N<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>\u2009\u2009(<\/mml:mo>N<\/mml:mi>\u2265<\/mml:mo>3<\/mml:mn>)<\/mml:mo><\/mml:math>is a bounded smooth domain. By using the perturbation method, we establish the existence of both positive and negative solutions for this system.<\/jats:p>","DOI":"10.1155\/2013\/431672","type":"journal-article","created":{"date-parts":[[2013,7,1]],"date-time":"2013-07-01T21:01:54Z","timestamp":1372712514000},"page":"1-9","source":"Crossref","is-referenced-by-count":0,"title":["Existence of Solutions for a Modified Nonlinear Schr\u00f6dinger System"],"prefix":"10.1155","volume":"2013","author":[{"given":"Yujuan","family":"Jiao","sequence":"first","affiliation":[{"name":"College of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730124, China"}]},{"given":"Yanli","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China"}]}],"member":"311","reference":[{"issue":"10","key":"18","doi-asserted-by":"crossref","first-page":"3262","DOI":"10.1143\/JPSJ.50.3262","volume":"50","year":"1981","journal-title":"Journal of the Physical Society of Japan"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1063\/1.525675"},{"issue":"10","key":"4","doi-asserted-by":"crossref","first-page":"3539","DOI":"10.1063\/1.860828","volume":"5","year":"1993","journal-title":"Physics of Fluids B"},{"issue":"14","key":"11","doi-asserted-by":"crossref","first-page":"2082","DOI":"10.1103\/PhysRevLett.70.2082","volume":"70","year":"1993","journal-title":"Physical Review Letters"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1007\/s002200050191"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.50.R687"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1007\/s005260100105"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0396(02)00064-5"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2003.09.008"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/BF00250555"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1081\/PDE-120037335"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2011.11.064"},{"issue":"2","key":"19","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/S0294-1449(16)30428-0","volume":"1","year":"1984","journal-title":"Annales de l'Institut Henri Poincar\u00e9"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2011.12.024"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/s000330050003"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/s002050050067"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/s002050100152"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-002-0191-8"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1999.3662"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1017\/S030821050002730X"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/S0294-1449(97)89296-7"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1996.3085"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(86)90096-0"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1007\/BF02161413"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1080\/03605308808820585"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-2012-11293-6"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-02-06783-7"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-0339-8_1"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1142\/S0219199708002958"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/431672.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/431672.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/431672.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,8]],"date-time":"2020-05-08T17:33:10Z","timestamp":1588959190000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/431672\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":29,"alternative-id":["431672","431672"],"URL":"https:\/\/doi.org\/10.1155\/2013\/431672","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}