In this paper, we study some properties of positive solutions of nonlinear integral equations with axis-symmetric kernels, which arise from weak-type convolution-Young's inequality and the stationary magnetic compressible uid stars. With the help of the method of moving planes and regularity lifting lemma, we show that all of the positive solutions in certain functional spaces are symmetric and monotonically decreasing on the axis of symmetry, and the integrable interval of positive solutions is also obtained. In addition, by analyzing the deca...
