{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T02:08:01Z","timestamp":1740103681273,"version":"3.37.3"},"reference-count":21,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,5,28]],"date-time":"2020-05-28T00:00:00Z","timestamp":1590624000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11761059","XBMU-2019-AB-34","31920200036"],"award-info":[{"award-number":["11761059","XBMU-2019-AB-34","31920200036"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Program for Yong Talent of State Ethnic Affairs Commission of 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\u2212<\/mml:mo>\u0394<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow>s<\/mml:mi><\/mml:mrow><\/mml:msup>u<\/mml:mi>\u2212<\/mml:mo>\u03bb<\/mml:mi>u<\/mml:mi>\/<\/mml:mo>x<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow>2<\/mml:mn>s<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:mrow><\/mml:mfenced>=<\/mml:mo>u<\/mml:mi><\/mml:mrow>r<\/mml:mi>\u2212<\/mml:mo>1<\/mml:mn><\/mml:mrow><\/mml:msup>+<\/mml:mo>\u03b4<\/mml:mi>g<\/mml:mi>u<\/mml:mi><\/mml:mrow><\/mml:mfenced>,<\/mml:mo><\/mml:mrow><\/mml:mtd>in\u2009<\/mml:mtext>\u03a9<\/mml:mi>,<\/mml:mo><\/mml:mrow><\/mml:mtd><\/mml:mtr>u<\/mml:mi>x<\/mml:mi><\/mml:mrow><\/mml:mfenced>><\/mml:mo>0<\/mml:mn>,<\/mml:mo><\/mml:mrow><\/mml:mtd>in\u2009<\/mml:mtext>\u03a9<\/mml:mi>,<\/mml:mo><\/mml:mrow><\/mml:mtd><\/mml:mtr>u<\/mml:mi>x<\/mml:mi><\/mml:mrow><\/mml:mfenced>=<\/mml:mo>0<\/mml:mn>,<\/mml:mo><\/mml:mrow><\/mml:mtd>in\u2009<\/mml:mtext>\u211d<\/mml:mi><\/mml:mrow>N<\/mml:mi><\/mml:mrow><\/mml:msup>\u2216<\/mml:mi>\u03a9<\/mml:mi>,<\/mml:mo><\/mml:mrow><\/mml:mtd><\/mml:mtr><\/mml:mtable><\/mml:mrow><\/mml:mfenced><\/mml:math> where \u03a9<\/mml:mi>\u2282<\/mml:mo>\u211d<\/mml:mi><\/mml:mrow>N<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:math> is a bounded Lipschitz domain with 0<\/mml:mn>\u2208<\/mml:mo>\u03a9<\/mml:mi><\/mml:math>, \u2212<\/mml:mo>\u0394<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow>s<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:math> is a fractional Laplace operator, s<\/mml:mi>\u2208<\/mml:mo>0,1<\/mml:mn><\/mml:mrow><\/mml:mfenced><\/mml:math>, N<\/mml:mi>><\/mml:mo>2<\/mml:mn>s<\/mml:mi><\/mml:math>, \u03b4<\/mml:mi><\/mml:math> is a positive number, 2<\/mml:mn><<\/mml:mo>r<\/mml:mi><<\/mml:mo>r<\/mml:mi>\u03bb<\/mml:mi>,<\/mml:mo>s<\/mml:mi><\/mml:mrow><\/mml:mfenced>\u2261<\/mml:mo>N<\/mml:mi>+<\/mml:mo>2<\/mml:mn>s<\/mml:mi>\u2212<\/mml:mo>2<\/mml:mn>\u03b1<\/mml:mi><\/mml:mrow>\u03bb<\/mml:mi><\/mml:mrow><\/mml:msub>\/<\/mml:mo>N<\/mml:mi>\u2212<\/mml:mo>2<\/mml:mn>s<\/mml:mi>\u2212<\/mml:mo>2<\/mml:mn>\u03b1<\/mml:mi><\/mml:mrow>\u03bb<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:mrow><\/mml:mfenced>+<\/mml:mo>1<\/mml:mn><\/mml:math>, \u03b1<\/mml:mi><\/mml:mrow>\u03bb<\/mml:mi><\/mml:mrow><\/mml:msub>\u2208<\/mml:mo>0<\/mml:mn>,<\/mml:mo>N<\/mml:mi>\u2212<\/mml:mo>2<\/mml:mn>s<\/mml:mi><\/mml:mrow><\/mml:mfenced>\/<\/mml:mo>2<\/mml:mn><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:mfenced><\/mml:math> is a parameter depending on \u03bb<\/mml:mi><\/mml:math>, 0<\/mml:mn><<\/mml:mo>\u03bb<\/mml:mi><<\/mml:mo>\u039b<\/mml:mi>N<\/mml:mi>,<\/mml:mo>s<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:math>, and \u039b<\/mml:mi>N<\/mml:mi>,<\/mml:mo>s<\/mml:mi><\/mml:mrow><\/mml:msub>=<\/mml:mo>2<\/mml:mn><\/mml:mrow>2<\/mml:mn>s<\/mml:mi><\/mml:mrow><\/mml:msup>\u0393<\/mml:mi>2<\/mml:mn><\/mml:mrow><\/mml:msup>N<\/mml:mi>+<\/mml:mo>2<\/mml:mn>s<\/mml:mi><\/mml:mrow><\/mml:mfenced>\/<\/mml:mo>4<\/mml:mn><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:mfenced><\/mml:mrow>\/<\/mml:mo>\u0393<\/mml:mi>2<\/mml:mn><\/mml:mrow><\/mml:msup>N<\/mml:mi>\u2212<\/mml:mo>2<\/mml:mn>s<\/mml:mi><\/mml:mrow><\/mml:mfenced>\/<\/mml:mo>4<\/mml:mn><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:math> is the sharp constant of the Hardy\u2013Sobolev inequality.<\/jats:p>","DOI":"10.1155\/2020\/5414309","type":"journal-article","created":{"date-parts":[[2020,5,28]],"date-time":"2020-05-28T23:33:43Z","timestamp":1590708823000},"page":"1-8","source":"Crossref","is-referenced-by-count":0,"title":["The Solvability of Fractional Elliptic Equation with the Hardy 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