American Institute of Mathematical Sciences

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June  2007, 6(2): 453-464. doi: 10.3934/cpaa.2007.6.453

The singularity analysis of solutions to some integral equations

Congming Li 1, and  Jisun Lim 2,

1. 

Department of Applied Mathematics, University of Colorado at Boulder, Boulder, CO 80309-0524
2. 

Department of Applied Mathematics, University of Colorado at Boulder, Campus Box 526, Boulder, CO 80309-0526

Received  January 2006 Revised  October 2006 Published  March 2007

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.
Keywords: Kelvin transform., Integral equations, singularities, asymptotic analysis.
Mathematics Subject Classification: Primary: 45E10, 45G05; Secondary: 35J9.
Citation: Congming Li, Jisun Lim. The singularity analysis of solutions to some integral equations. Communications on Pure & Applied Analysis, 2007, 6 (2) : 453-464. doi: 10.3934/cpaa.2007.6.453
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