This paper is devoted to studying the existence of positive solutions for the following integral system
$$\left\{ {\begin{array}{*{20}{c}}
{u\left( x \right) = \int_{{\mathbb{R}^n}} {{{\left| {x - y} \right|}^\lambda }{v^{ - q}}\left( y \right)dy,} } \\
{v\left( x \right) = \int_{{\mathbb{R}^n}} {{{\left| {x - y} \right|}^\lambda }{u^{ - p}}\left( y \right)dy,} }
\end{array}} \right.p,q > 0,\lambda \in \left( {0,\infty } \right),n \geqslant 1$$
. It is shown that if (u, v) is a pair of positive Lebesgue measurable solutions of this integral system, then
$$\frac{1}{{p -...
