{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T21:49:09Z","timestamp":1758404949056,"version":"3.40.5"},"reference-count":24,"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":["11361054","20126203110004","1208RJZA258"],"award-info":[{"award-number":["11361054","20126203110004","1208RJZA258"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Specialized Research Fund for the Doctoral Program","award":["11361054","20126203110004","1208RJZA258"],"award-info":[{"award-number":["11361054","20126203110004","1208RJZA258"]}]},{"name":"Gansu Provincial National Science Foundation of China","award":["11361054","20126203110004","1208RJZA258"],"award-info":[{"award-number":["11361054","20126203110004","1208RJZA258"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"We consider the equations involving the one-dimensional p<\/mml:mi><\/mml:mrow><\/mml:math>-Laplacian (<\/mml:mo>P<\/mml:mi>)<\/mml:mo>:<\/mml:mtext><\/mml:math>\u2009\u2009(<\/mml:mo>u<\/mml:mi><\/mml:mrow>\u2032<\/mml:mi><\/mml:mrow><\/mml:msup>t<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:mfenced><\/mml:mrow>p<\/mml:mi>-<\/mml:mo>2<\/mml:mn><\/mml:mrow><\/mml:msup>u<\/mml:mi><\/mml:mrow>\u2032<\/mml:mi><\/mml:mrow><\/mml:msup>(<\/mml:mo>t<\/mml:mi>)<\/mml:mo>)<\/mml:mo><\/mml:mrow>\u2032<\/mml:mi><\/mml:mrow><\/mml:msup>+<\/mml:mo>\u03bb<\/mml:mi>f<\/mml:mi>(<\/mml:mo>u<\/mml:mi>(<\/mml:mo>t<\/mml:mi>)<\/mml:mo>)<\/mml:mo>=<\/mml:mo>0<\/mml:mn><\/mml:math>, 0<\/mml:mn><<\/mml:mo>t<\/mml:mi><<\/mml:mo>1<\/mml:mn>,<\/mml:mo><\/mml:math> and \n u<\/mml:mi>(<\/mml:mo>0<\/mml:mn>)<\/mml:mo>=<\/mml:mo>u<\/mml:mi>(<\/mml:mo>1<\/mml:mn>)<\/mml:mo>=<\/mml:mo>0<\/mml:mn>,<\/mml:mo><\/mml:math> where p<\/mml:mi>><\/mml:mo>1<\/mml:mn>,<\/mml:mo>\u03bb<\/mml:mi>><\/mml:mo>0<\/mml:mn>,<\/mml:mo>f<\/mml:mi>\u2208<\/mml:mo>C<\/mml:mi><\/mml:mrow>1<\/mml:mn><\/mml:mrow><\/mml:msup>(<\/mml:mo>R<\/mml:mi>;<\/mml:mo>R<\/mml:mi>)<\/mml:mo>,<\/mml:mo>f<\/mml:mi>(<\/mml:mo>s<\/mml:mi>)<\/mml:mo>s<\/mml:mi>><\/mml:mo>0<\/mml:mn>,<\/mml:mo><\/mml:math> and \n s<\/mml:mi>\u2260<\/mml:mo>0<\/mml:mn><\/mml:math>. We show the existence of sign-changing solutions under the assumptions f<\/mml:mi><\/mml:mrow>\u221e<\/mml:mi><\/mml:mrow><\/mml:msub>=<\/mml:mo>l<\/mml:mtext>i<\/mml:mtext>m<\/mml:mtext><\/mml:mrow>|<\/mml:mo>s<\/mml:mi>|<\/mml:mo>\u2192<\/mml:mo>\u221e<\/mml:mi><\/mml:mrow><\/mml:msub>\u2061<\/mml:mo>(<\/mml:mo>f<\/mml:mi>s<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow>\/<\/mml:mo>s<\/mml:mi><\/mml:mrow>p<\/mml:mi>-<\/mml:mo>1<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:mrow>)<\/mml:mo>=<\/mml:mo>+<\/mml:mo>\u221e<\/mml:mi><\/mml:math> and f<\/mml:mi><\/mml:mrow>0<\/mml:mn><\/mml:mrow><\/mml:msub>=<\/mml:mo>l<\/mml:mtext>i<\/mml:mtext>m<\/mml:mtext><\/mml:mrow>|<\/mml:mo>s<\/mml:mi>|<\/mml:mo>\u2192<\/mml:mo>0<\/mml:mn><\/mml:mrow><\/mml:msub>(<\/mml:mo>f<\/mml:mi>(<\/mml:mo>s<\/mml:mi>)<\/mml:mo><\/mml:mrow>\/<\/mml:mo>s<\/mml:mi><\/mml:mrow>p<\/mml:mi>-<\/mml:mo>1<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:mrow>)<\/mml:mo>\u2208<\/mml:mo>[<\/mml:mo>0<\/mml:mn>,<\/mml:mo>\u221e<\/mml:mi>]<\/mml:mo><\/mml:math>. We also show that (<\/mml:mo>P<\/mml:mi>)<\/mml:mo><\/mml:math> has exactly one solution having specified nodal properties for \u03bb<\/mml:mi>\u2208<\/mml:mo>(<\/mml:mo>0<\/mml:mn>,<\/mml:mo>\u03bb<\/mml:mi><\/mml:mrow>*<\/mml:mi><\/mml:mrow><\/mml:msup>)<\/mml:mo><\/mml:math> for some \u03bb<\/mml:mi><\/mml:mrow>*<\/mml:mi><\/mml:mrow><\/mml:msup>\u2208<\/mml:mo>(<\/mml:mo>0<\/mml:mn>,<\/mml:mo>\u221e<\/mml:mi>)<\/mml:mo><\/mml:math>. Our main results are based on quadrature method.<\/jats:p>","DOI":"10.1155\/2014\/810193","type":"journal-article","created":{"date-parts":[[2014,8,17]],"date-time":"2014-08-17T17:08:20Z","timestamp":1408295300000},"page":"1-9","source":"Crossref","is-referenced-by-count":1,"title":["Existence of Sign-Changing Solutions to Equations Involving the One-Dimensional p<\/mml:mi><\/mml:mrow><\/mml:math>-Laplacian"],"prefix":"10.1155","volume":"2014","author":[{"given":"Ruyun","family":"Ma","sequence":"first","affiliation":[{"name":"Department of Mathematics, Northwest Normal University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lingfang","family":"Jiang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Northwest Normal University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"doi-asserted-by":"publisher","key":"1","DOI":"10.2307\/2160465"},{"doi-asserted-by":"publisher","key":"2","DOI":"10.1006\/jmaa.1997.5334"},{"doi-asserted-by":"publisher","key":"3","DOI":"10.1512\/iumj.1971.20.20001"},{"doi-asserted-by":"publisher","key":"4","DOI":"10.1016\/0362-546X(93)90169-S"},{"doi-asserted-by":"publisher","key":"5","DOI":"10.1016\/j.jmaa.2004.09.002"},{"doi-asserted-by":"publisher","key":"6","DOI":"10.1016\/j.na.2005.12.036"},{"doi-asserted-by":"publisher","key":"7","DOI":"10.1016\/j.jde.2006.03.021"},{"doi-asserted-by":"publisher","key":"8","DOI":"10.1090\/S0002-9939-97-04148-8"},{"doi-asserted-by":"publisher","key":"9","DOI":"10.1016\/S0362-546X(99)00143-1"},{"issue":"132","key":"10","volume":"2004","year":"2004","journal-title":"Electronic Journal of Differential Equations"},{"issue":"3","key":"11","first-page":"83","volume":"7","year":"2000","journal-title":"Communications on Applied Nonlinear Analysis"},{"doi-asserted-by":"publisher","key":"12","DOI":"10.1016\/0362-546X(94)90245-3"},{"doi-asserted-by":"publisher","key":"13","DOI":"10.1016\/j.na.2006.12.015"},{"doi-asserted-by":"publisher","key":"14","DOI":"10.1155\/S1025583497000040"},{"doi-asserted-by":"publisher","key":"15","DOI":"10.1007\/BF03323111"},{"doi-asserted-by":"publisher","key":"16","DOI":"10.1017\/S0308210511000126"},{"doi-asserted-by":"publisher","key":"17","DOI":"10.3934\/dcds.2007.17.143"},{"doi-asserted-by":"publisher","key":"18","DOI":"10.1007\/s11117-005-0002-5"},{"doi-asserted-by":"publisher","key":"19","DOI":"10.1017\/S0308210500014670"},{"doi-asserted-by":"publisher","key":"20","DOI":"10.1006\/jmaa.1996.0400"},{"doi-asserted-by":"publisher","key":"21","DOI":"10.1512\/iumj.2004.53.2396"},{"doi-asserted-by":"publisher","key":"22","DOI":"10.1016\/0362-546X(81)90096-1"},{"doi-asserted-by":"publisher","key":"23","DOI":"10.1016\/0362-546X(93)90020-S"},{"issue":"4","key":"24","first-page":"575","volume":"7","year":"1998","journal-title":"Dynamic Systems an Applications"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/810193.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/810193.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/810193.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,12,4]],"date-time":"2016-12-04T16:02:15Z","timestamp":1480867335000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/jam\/2014\/810193\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":24,"alternative-id":["810193","810193"],"URL":"https:\/\/doi.org\/10.1155\/2014\/810193","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}