Liouville Type Theorems for General Integral System with Negative Exponents

In this paper, we establish a Liouville type theorem for the following integral system with negative exponents {u(x) = integral(Rn) vertical bar x - y vertical bar(nu) f(u, v) (y) dy, x is an element of R-n, v(x) = integral(Rn) vertical bar x - y vertical bar(nu) g(u, v) (y) dy, x is an element of R-n, where n >= 1, nu > 0, and f, g are continuous functions defined on R+ X R+. Under nature structure conditions on f and g, we classify each pair of positive solutions for above integral system by using the method of moving sphere in integral forms. Moreover, some other Liouville theorems are established for similar integral systems.