The singularity analysis of solutions to some integral equations

Congming Li; Jisun Lim

doi:10.3934/cpaa.2007.6.453

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2007, Volume 6, Issue 2: 453-464. Doi: 10.3934/cpaa.2007.6.453

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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: June 2007

Abstract / Introduction Related Papers Cited by

Abstract

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.

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Mathematics Subject Classification: Primary: 45E10, 45G05; Secondary: 35J99.

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