Abstract
We establish a 3G-theorem for the iterated Green function of (-Delta)(pm), (p >= 1, m > 1), on the unit ball B of R-n (n >= 1) with boundary conditions (partial derivative/partial derivative nu)(j)(-Delta)(km)u = 0 on partial derivative B, for 0 <= k <= p - 1 and 0 <= j <= m - 1. We exploit this result to study a class of potentials J(m,n)((p)). Next, we aim at proving the existence of positive continuous solutions for the following polyharmonic nonlinear problems (-Delta)(pm)u = h(center dot, u), in D (in the sense of distributions), lim(vertical bar x vertical bar -> 1)((-Delta)(km)u(x)/(1-vertical bar x vertical bar)(m-1)) = 0, for 0 <= k <= p - 1, where D = B or B\{0} and h is a Borel measurable function on D x (0,infinity) satisfying some appropriate conditions related to J(m,n)((p)). Copyright (c) 2006 Imed Bachar.