Acta mathematica scientia, Series B >
REGULARITY AND SYMMETRY OF SOLUTIONS OF AN INTEGRAL SYSTEM
Received date: 2011-07-04
Revised date: 2011-10-08
Online published: 2012-09-20
Supported by
Chen research is supported by NSF of China (10961015) and Yang research is supported by NSF of China (10961016); the GAN PO555 Program of Jiangxi.
In this paper, we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system
u(x) = ∫Rn G (x − y)v(y)q/|y| dy, v(x) = ∫Rn G (x − y)u(y)p/|y| dy
for x ∈ Rn, where G (x) is the kernel of Bessel potential of order α, 0 ≤β < α< n, 1 < p, q < n− β/β and 1 /p + 1+1/q + 1>n −α + β/n.
We show that positive solution pairs (u, v) ∈ Lp+1(Rn)×Lq+1(Rn) are H¨older continuous, radially symmetric and strictly decreasing about the origin.
Key words： regularity; radially symmetry; Bessel kernel; nonlinear integral system
CHEN Xiao-Li , YANG Jian-Fu . REGULARITY AND SYMMETRY OF SOLUTIONS OF AN INTEGRAL SYSTEM[J]. Acta mathematica scientia, Series B, 2012 , 32(5) : 1759 -1780 . DOI: 10.1016/S0252-9602(12)60139-8
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