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The Liouville type theorem and local regularity results for nonlinear differential and integral systems

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  • In this paper we establish a Liouville type theorem for positive solutions of a class of system of integral equations. Firstly, we show the local regularity lifting result with the help of the Hardy-Littlewood-Sobolev inequality. Then by the method of moving planes in integral forms, we obtain a Liouville type theorem for this system.
    Mathematics Subject Classification: Primary: 35A05, 35J45, 35J60; Secondary: 45G15.

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