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Existence of solutions to the supercritical Hardy-Littlewood-Sobolev system with fractional Laplacians

  • * Corresponding author: Changfeng Gui

    * Corresponding author: Changfeng Gui 

The authors are supported by NSF DMS-1601885

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  • It is known that the supercritical Hardy-Littlewood-Sobolev (HLS) systems with an integer power of Laplacian admit classic solutions. In this paper, we prove that the supercritical HLS systems with fractional Laplacians $ (-Δ)^s $, $ s∈(0,1) $, also admit classic solutions.

    Mathematics Subject Classification: Primary: 35R11, 35R09; Secondary: 45G15.


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