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• W3083452103 endingPage "112102" @default.
• W3083452103 startingPage "112102" @default.
• W3083452103 abstract "Using the Mountain-Pass Theorem of Ambrosetti and Rabinowitz we prove that the following fractional p-Laplacian equation with double critical nonlinearities (−Δp)su=|u|ps∗−2u+|u|ps∗(α)−2u|x|αinRN,admits a positive solution in the class Ẇs,p(RN). In the above, (−Δp)s is the fractional p-Laplacian, s∈(0,1), p>1, 0<α<ps<N, ps∗=NpN−ps is the critical fractional Sobolev exponent and ps∗(α)=p(N−α)N−ps is the critical Hardy–Sobolev exponent, Ẇs,p(RN) denotes the completion of C0∞(RN) with respect to Gagliardo norm [u]s,pp≔∫RN∫RN|u(x)−u(y)|p|x−y|N+psdxdy.Our method is based on the existence of extremals of some fractional Hardy–Sobolev type inequalities, and coupled with some intricate estimates for the nonlocal (s,p)-gradient. Moreover, we also establish the existence of a nontrivial solution to an elliptic system which involves fractional p-Laplacian and critical Hardy–Sobolev exponents in RN." @default.
• W3083452103 created "2020-09-11" @default.
• W3083452103 creator A5031011384 @default.
• W3083452103 date "2021-01-01" @default.
• W3083452103 modified "2023-10-02" @default.
• W3083452103 title "Existence of solutions to elliptic problems with fractional p-Laplacian and multiple critical nonlinearities in the entire space<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline id=d1e22 altimg=si14.svg><mml:msup><mml:mrow><mml:mi mathvariant=double-struck>R</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup></mml:math>" @default.
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• W3083452103 doi "https://doi.org/10.1016/j.na.2020.112102" @default.
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