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Symmetry of solutions to some systems of integral equations. (English) Zbl 1156.45300
Summary: We study some systems of integral equations, including those related to Hardy-Littlewood-Sobolev inequalities. We prove that, under some integrability conditions, the positive regular solutions to the systems are radially symmetric and monotone about some point. In particular, we establish the radial symmetry of the solutions to the Euler-Lagrange equations associated with the classical and weighted Hardy-Littlewood-Sobolev inequality.

45E10Integral equations of the convolution type
45G15Systems of nonlinear integral equations
45G05Singular nonlinear integral equations
26D10Inequalities involving derivatives, differential and integral operators
45M20Positive solutions of integral equations
35J60Nonlinear elliptic equations
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