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The singularity analysis of solutions to some integral equations

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  • We consider a system of Euler-Lagrange equations associated with the weighted Hardy-Littlewood-Sobolev inequality in $R^n$. We demonstrate that the positive solutions of the system of Euler-Lagrange equations are asymptotic to certain forms of limit around the center and near infinity, respectively. The results are proven using the optimal integrability conditions for the positive solutions of the system of equations.
    Mathematics Subject Classification: Primary: 45E10, 45G05; Secondary: 35J99.

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