Abstract
By developing the direct method of moving planes, we study the radial symmetry of nonnegative solutions for a fractional Laplacian system with different negative powers: (-Delta)alpha 2u(x)+u-gamma(x)+v-q(x)=0,x is an element of RN, (-Delta)beta(2)v(x)+v-sigma(x)+u-p(x)=0,x is an element of RN, u(x)greater than or similar to|x|a,v(x)greater than or similar to|x|bas|x|->infinity, where alpha,beta is an element of(0,2), and a,b>0 are constants. We study the decay at infinity and narrow region principle for the fractional Laplacian system with different negative powers. The same results hold for nonlinear Henon-type fractional Laplacian systems with different negative powers.