Existence results for some polyharmonic problems in the half-space

We study the existence of positive solutions of the m-polyharmonic nonlinear elliptic equation m(−Δ)u+f(⋅,u)=0 in the half-space , n⩾2 and m⩾1. Our purpose is to give two existence results for the above equation subject to some boundary conditions, where the nonlinear term f(x,t) satisfies some appropriate conditions related to a certain Kato class of functions .