Higher-order evolution inequalities with Hardy potential on the Kor\'{a}nyi ball

We consider a higher order in (time) semilinear evolution inequality posed on the Kor\'{a}nyi ball under an inhomogeneous Dirichlet-type boundary condition. The problem involves an inverse-square potential λ/|ξ|H², where λ ≥ -(Q-2)²/4 and a general weight function V depending on the space variable in front of the power nonlinearity. We first establish a general nonexistence result for the considered problem. Next, in the special case V(ξ):=|ξ|Hᵃ, a∈ R, we prove the sharpness of our nonexistence result and show that the problem admits three different critical behaviors according to the value of the parameter λ.