Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 134, Issue 6, Pages 1661-1670Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9939-05-08411-X
Keywords
Hardy-Littlewood-Sobolev inequalities; systems of integral equations; radial symmetry; classification of solution
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In this paper, we study some systems of integral equations, including those related to Hardy-Littlewood-Sobolev (HLS) 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 established the radial symmetry of the solutions to the Euler-Lagrange equations associated with the classical and weighted Hardy-Littlewood-Sobolev inequality.
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