It is quite usual to transform elliptic PDE problems of second order into fixed point integral problems, via the Green’s function. But it is not easy, in general, to handle integrals involved in such a formulation. When it comes to the Laplacian operator on balls of Rn, we give here a radially symmetrical Green’s function which, under some nonlinearity assumptions, makes the Green’s Integral representation formula easier to use; we give three examples of application.