{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:19:16Z","timestamp":1746803956671,"version":"3.40.5"},"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":["11371289","201206285005"],"award-info":[{"award-number":["11371289","201206285005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["11371289","201206285005"],"award-info":[{"award-number":["11371289","201206285005"]}],"id":[{"id":"10.13039\/501100004543","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>The existence of weak solution for<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>p<\/mml:mi><\/mml:mrow><\/mml:math>-Laplace problem is studied in the paper. By exploiting the relationship between the Nehari manifold and fibering maps and combining the compact imbedding theorem and the behavior of Palais-Smale sequences in the Nehari manifold, the existence of weak solutions is established. By means of the Arzela-Ascoli fixed point theorem, some existence results of the corresponding time-fractional equations of the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>p<\/mml:mi><\/mml:mrow><\/mml:math>-Laplace problem are obtained.<\/jats:p>","DOI":"10.1155\/2014\/231892","type":"journal-article","created":{"date-parts":[[2014,7,2]],"date-time":"2014-07-02T17:08:11Z","timestamp":1404320891000},"page":"1-9","source":"Crossref","is-referenced-by-count":2,"title":["Existence of Weak Solutions for Nonlinear Time-Fractional<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>p<\/mml:mi><\/mml:mrow><\/mml:math>-Laplace Problems"],"prefix":"10.1155","volume":"2014","author":[{"given":"Meilan","family":"Qiu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}]},{"given":"Liquan","family":"Mei","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"Department of Chemical & Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB, Canada T2N 1N4"}]}],"member":"311","reference":[{"year":"1998","key":"1"},{"doi-asserted-by":"publisher","key":"2","DOI":"10.1016\/S0022-247X(02)00716-3"},{"doi-asserted-by":"publisher","key":"3","DOI":"10.1016\/j.jmaa.2010.04.034"},{"doi-asserted-by":"publisher","key":"4","DOI":"10.1016\/j.na.2010.11.005"},{"doi-asserted-by":"publisher","key":"5","DOI":"10.1515\/9783110804775"},{"year":"2009","key":"6"},{"doi-asserted-by":"publisher","key":"7","DOI":"10.1016\/S0022-0396(03)00121-9"},{"doi-asserted-by":"publisher","key":"8","DOI":"10.1016\/j.na.2007.01.004"},{"doi-asserted-by":"publisher","key":"9","DOI":"10.1007\/s00526-004-0289-2"},{"doi-asserted-by":"publisher","key":"10","DOI":"10.1006\/jdeq.1998.3440"},{"issue":"5","key":"11","first-page":"1","volume":"1997","year":"1997","journal-title":"Electronic Journal of Differential Equations"},{"doi-asserted-by":"publisher","key":"12","DOI":"10.1016\/S0362-546X(99)00118-2"},{"key":"26","first-page":"127","volume":"31","year":"2008","journal-title":"Journal of Sichuan Normal University"},{"volume":"198","year":"1999","series-title":"Mathematics in Science and Engineering","key":"14"},{"year":"2009","key":"15"},{"doi-asserted-by":"publisher","key":"16","DOI":"10.1016\/j.camwa.2009.06.029"},{"year":"1993","key":"17"},{"year":"1993","key":"18"},{"doi-asserted-by":"publisher","key":"19","DOI":"10.1155\/2009\/314656"},{"volume":"36","year":"2006","journal-title":"Electronic Journal of Differential Equations","key":"20"},{"doi-asserted-by":"publisher","key":"21","DOI":"10.1016\/j.jmaa.2005.02.052"},{"doi-asserted-by":"publisher","key":"24","DOI":"10.1017\/S0308210500023787"},{"volume":"204","year":"2006","series-title":"North-Holland Mathematics Studies","key":"25"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/231892.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/231892.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/231892.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,18]],"date-time":"2016-08-18T11:31:58Z","timestamp":1471519918000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/231892\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":23,"alternative-id":["231892","231892"],"URL":"https:\/\/doi.org\/10.1155\/2014\/231892","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}