Abstract
Here we study the polyharmonic nonlinear elliptic boundary value problem on the unit ball B in R-n ( n >= 2) (- Delta)(m) u + g(., u) = 0, in B ( in the sense of distributions) lim(x ->xi is an element of partial derivative B)(u( x)/( 1-| x|(2))(m- 1)) = 0(xi). Under appropriate conditions related to a Kato class on the nonlinearity g( x, t), we give some existence results. Our approach is based on estimates for the polyharmonic Green function on B with zero Dirichlet boundary conditions, including a 3G-theorem, which leeds to some useful properties on functions belonging to the Kato class.