A Liouville theorem for high order degenerate elliptic equations

In this paper, we apply the method of moving plane to the following high order degenerate elliptic equation,(−A)pu=uαin R+n+1,n≥1, where the operator A=y∂y2+a∂y+Δx, a≥1a≥1. We get a Liouville theorem for subcritical case and classify the solutions for the critical case.