Acta mathematica scientia, Series B >
CLASSIFICATION OF SOLUTIONS FOR A CLASS OF SINGULAR INTEGRAL SYSTEM
Received date: 2009-07-06
Online published: 2011-07-20
Supported by
Supported by National Natural Science Foundation of China-NSAF (10976026).
In this paper, we consider the following integral system:
???u(x) = v (y) dy,
? n n-α
R |x-y|
(1.1)
??? up(y)
?v(x) = n-μdy,
n
R |x-y|
where 0 < α, μ < n; p,q ≥ 1. Using the method of moving planes in an integral form which
was recently introduced by Chen, Li, and Ou in [2, 4, 8], we show that all positive solutions
of (0.1) are radially symmetric and decreasing with respect to some point under some
general conditions of integrability. The results essentially improve and extend previously
known results [4, 8].
XU Jian-Kai , TAN Zhong . CLASSIFICATION OF SOLUTIONS FOR A CLASS OF SINGULAR INTEGRAL SYSTEM[J]. Acta mathematica scientia, Series B, 2011 , 31(4) : 1449 -1456 . DOI: 10.1016/S0252-9602(11)60330-5
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