Some properties of positive solutions for an integral system with the double weighted Riesz potentials
2016
In this paper, we study some important properties of positive
solutions for a nonlinear integral system. With the help of the
method of moving planes in an integral form, we show that under
certain integrable conditions, all of positive solutions to this
system are radially symmetric and decreasing with respect to the
origin. Meanwhile, using the regularity lifting lemma, which was
recently introduced by Chen and Li in [1], we obtain the
optimal integrable intervals and sharp asymptotic behaviors for such
positive solutions, which characterize the closeness of system to
some extent.
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