Existence results for some polyharmonic problems in the half-space

We study the existence of positive solutions of them-polyharmonic nonlinear elliptic equation (−Δ)mu+ f (·,u) = 0 in the half-space Rn + := {x = (x1, . . . , xn) ∈ Rn: xn > 0}, 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 K∞m,n(Rn +). © 2005 Elsevier Inc. All rights reserved.