Positive solutions to integral systems with weight and Bessel potentials

In this paper, we consider the integral system with weight and the Bessel potentials:{u(x)=∫Rngα(x−y)u(y)pv(y)q|y|σdy,v(x)=∫Rngα(x−y)v(y)pu(y)q|y|σdy, where u,v>0u,v>0, σ⩾0σ⩾0, 0<α