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Symmetry and monotonicity for a system of integral equations

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  • In this paper, we consider radial symmetry of positive solutions for a system of three integral equations in $R^n$. Under some mild integrability conditions, we prove that all the solutions are radially symmetric and monotone decreasing about some point. This generalizes a recent result of Chen, Li, and Ou [4]. To establish the symmetry, we use an integral form of the method of moving planes which is quite different from the traditional method of moving planes for PDEs. We also generalize our result to a system containing any number of integral equations.
    Mathematics Subject Classification: 35J99, 45E10.


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