Article ID Journal Published Year Pages File Type
4664110 Acta Mathematica Scientia 2012 22 Pages PDF
Abstract

In this paper, we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system u(x)=∫RnGα(x−y)v(y)q|y|βdy,      v(x)=∫RnGα(x−y)u(y)p|y|βdy for x∈ℝnx∈ℝn, where Gα(x) is the kernel of Bessel potential of order α, 0 ≤ β < α < n, 1 <, p, q   < n−ββ and 1p+1+1q+1>n−α+βn. We show that positive solution pairs (u, v) ∈ Lp+1(ℝn)×Lq+1(ℝn) are Hölder continuous, radially symmetric and strictly decreasing about the origin.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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