We will study the following polyharmonic nonlinear elliptic equation (-Delta)(m)u+ f ((.), u)= 0 in R-n, n > 2m. Under appropriate conditions on the nonlinearity f (x, t), related to a class of functions called m-Green-tight functions, we give some existence results for the above equation. Copyright (c) 2006 H. Maagli and M. Zribi.