Radial symmetry and asymptotic behaviors of positive solutions for certain nonlinear integral equations

In this paper, we investigate some properties of positive solutions for a nonlinear integral system. Using the method of moving planes in an integral form, which was recently introduced by Chen, Li, and Ou in Chen et al. (2005, 2006) [2] and [3], we show that all positive solutions of the integral system in certain functional spaces are radially symmetric with respect to the origin and decreasing in critical space. Furthermore, with the help of regularity lifting lemma, we obtain the optimal integrable intervals and the asymptotic estimates for such solutions around the origin and near infinity.