Qualitative properties of solutions to an integral system associated with the bessel potential

In this paper, we study a differential system associated with the Bessel potential: [EQUATION PRESENTED] is the Laplacian operator in Rn. Under some appropriate conditions, this di erential system is equivalent to an integral system of the Bessel potential type. By the regularity lifting method developed in [4] and [18], we obtain the regularity of solutions to the integral system. We then apply the moving planes method to obtain radial symmetry and monotonicity of positive solutions. We also establish the uniqueness theorem for radially symmetric solutions. Our nonlinear terms f1(u(x); v(x)) and f2(u(x); v(x)) are quite general and our results extend the earlier ones even in the case of single equation substantially.