A Liouville theorem for high order degenerate elliptic equations (Q2254015)

The authors develop moving plane techniques for higher order degenerate equations in the form \[ (-A)^pu= u^\alpha\quad\text{ in }\mathbb R^{N+1}_+, n\geq 1, \] where \(A\equiv y\partial_y^2+a\partial_y+\Delta_x\), \(a\geq 1\). In particular, Liouville type theorems are obtained for subcritical exponents and a classification of solutions is given in the supercritical range.