Abstract
Let G(m,n)(D) be the Green function of (-Delta)(m), m >= 1, on the complementary D of the unit closed ball in R-n, n >= 2, with Dirichlet boundary conditions (partial derivative/partial derivative nu)(j) =0, 0 <= j <= m-1. We establish some estimates on G(m,n)(D) including the 3G- Inequality given by (1.3). Next, we introduce a polyharmonic Kato class of functions K-m,n(infinity)(D) and we exploit the properties of this class to study the existence of positive solutions of some polyharmonic nonlinear elliptic problems.