Classification of solutions for a system of integral equations

Under the natural integrability conditions u is an element of LP+1 (R-n) and v is an element of Lq+1 (R-n), we prove that all the solutions are radially symmetric and monotonic decreasing about some point. To prove this result, we introduce an integral form of the method of moving planes that is quite different front the traditional method of moving planes for PDES. We expect to see applications of this new method to many problems.