Liouville theorems of solutions to mixed order Henon-Hardy type system with exponential nonlinearity

In this paper, we are concerned with the Henon-Hardy type systems with exponential nonlinearity on a half space R-+(2) {(-Delta)(alpha/2)2 u(x) = vertical bar x vertical bar(a)u(p1) (x)e(q1 nu(x)), x is an element of R-+(2), (-Delta)nu(x) = vertical bar x vertical bar(b)u(p2)(x)e(q2 nu(x)), x is an element of R-+(2), with Dirichlet boundary conditions, where 0 < alpha < 2 and p(1), p(2), q(1), q(2) > 0. First, we derived the integral representation formula corresponding to the above system under the assumption p(1) >= - 2a/alpha - 1. Then, we prove Liouville theorem for solutions to the above system via the method of scaling spheres.