{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:19Z","timestamp":1740134539868,"version":"3.37.3"},"reference-count":23,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"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":["11301059","11361054","13YJA790078"],"award-info":[{"award-number":["11301059","11361054","13YJA790078"]}],"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":["11301059","11361054","13YJA790078"],"award-info":[{"award-number":["11301059","11361054","13YJA790078"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002338","name":"Ministry of Education of the People\u2019s Republic of China","doi-asserted-by":"publisher","award":["11301059","11361054","13YJA790078"],"award-info":[{"award-number":["11301059","11361054","13YJA790078"]}],"id":[{"id":"10.13039\/501100002338","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Let<jats:italic>X<\/jats:italic>be a Banach space and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msub><mml:mi>C<\/mml:mi><mml:mi>n<\/mml:mi><\/mml:msub><\/mml:mrow><\/mml:math>a family of connected subsets of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>R<\/mml:mi><mml:mo>\u00d7<\/mml:mo><mml:mi>X<\/mml:mi><\/mml:mrow><\/mml:math>. We prove the existence of unbounded components in superior limit of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mo>{<\/mml:mo><mml:msub><mml:mi>C<\/mml:mi><mml:mi>n<\/mml:mi><\/mml:msub><mml:mo>}<\/mml:mo><\/mml:mrow><\/mml:math>, denoted by<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mover accent=\"true\"><mml:mtext>lim<\/mml:mtext><mml:mo>\u00af<\/mml:mo><\/mml:mover><\/mml:mrow><\/mml:math>\u2009<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:msub><mml:mi>C<\/mml:mi><mml:mi>n<\/mml:mi><\/mml:msub><\/mml:mrow><\/mml:math>, which have prescribed shapes. As applications, we investigate the global behavior of the set of positive periodic solutions to nonlinear first-order differential equations with delay, which can be used for modeling physiological processes.<\/jats:p>","DOI":"10.1155\/2014\/780486","type":"journal-article","created":{"date-parts":[[2014,4,6]],"date-time":"2014-04-06T17:05:26Z","timestamp":1396803926000},"page":"1-7","source":"Crossref","is-referenced-by-count":2,"title":["The Existence and Application of Unbounded Connected Components"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6643-5299","authenticated-orcid":true,"given":"Hua","family":"Luo","sequence":"first","affiliation":[{"name":"School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian 116025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruyun","family":"Ma","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Northwest Normal University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"crossref","first-page":"45","DOI":"10.24033\/asens.836","volume":"51","year":"1934","journal-title":"Annales Scientifiques de l'\u00c9cole Normale Sup\u00e9rieure"},{"key":"2","first-page":"183","volume":"4","year":"1960","journal-title":"Summa Brasiliensis Mathematicae"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(81)90171-2"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(84)90069-7"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-8641(01)00301-7"},{"year":"1958","key":"6"},{"issue":"2","key":"7","doi-asserted-by":"crossref","first-page":"279","DOI":"10.12775\/TMNA.2009.043","volume":"34","year":"2009","journal-title":"Topological Methods in Nonlinear Analysis"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1038\/287017a0"},{"issue":"4300","key":"12","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1126\/science.267326","volume":"197","year":"1977","journal-title":"Science"},{"key":"13","first-page":"23","volume":"6","year":"1976","journal-title":"Matematyka Stosowana"},{"key":"14","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/0022-0396(74)90084-9","volume":"15","year":"1974","journal-title":"Journal of Differential Equations"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1137\/0523035"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2007.07.017"},{"key":"17","first-page":"1","volume":"59","year":"2001","journal-title":"Electronic Journal of Differential Equations"},{"issue":"6","key":"18","first-page":"715","volume":"20","year":"1999","journal-title":"Chinese Annals of Mathematics A"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2005.03.084"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2008.05.007"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2004.02.018"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2010.01.015"},{"year":"1985","key":"23"},{"year":"1988","key":"24"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1007\/BF00281748"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4838-5"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/780486.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/780486.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/780486.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T07:06:48Z","timestamp":1498115208000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/780486\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":23,"alternative-id":["780486","780486"],"URL":"https:\/\/doi.org\/10.1155\/2014\/780486","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}