期刊
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
卷 134, 期 6, 页码 1661-1670出版社
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9939-05-08411-X
关键词
Hardy-Littlewood-Sobolev inequalities; systems of integral equations; radial symmetry; classification of solution
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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