A class of fractional order Laplace equations with the following form was studied by the di-rect moving plane method:(-Δ)α/2 u(x)= |x|βup(x)+|x|γuq(x),x∈Rn,0<α<2,n≥3.The radial symmetry of the positive solution of the equation in the whole space and under different con-straints is obtained.
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