In this paper,we consider the semilinear equation involving the fractional Laplacian in the Euclidian space R^n:(-△)^(α/2)u(x) = f(x_n)u^p(x),x ∈ R^n(0.1)in the subcritical case with 1 < p <(n+α)/(n-α).Instead of carrying out direct investigations on pseudo-differential equation(0.1),we first seek its equivalent form in an integral equation as below:u(x) = ∫R^n G∞(x,y) f(y_n) u^p(y)dy,(0.2)where G∞(x,y) is the Green's function associated with the fractional Laplacian in R^n.Employing the method of moving planes in integral forms,we are able to derive the nonexistence of positive solutions for(0.2) in the subcritical case.Thanks to the equivalence,same conclusion is true for(0.1).
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