The aim of this paper is to obtain nonlinear operators in suitable spaces whise fixed point coincide with the solutions of the nonlinear boundary value problems (

(

'))'=f(t, u, u'), l(u, u') = 0, where l(u, u')=0 denotes the Dirichlet, Neumann or periodic boundary conditions on [0, T],

: N N is a suitable monotone monotone homemorphism and f:[0, T] N N is a Caratheodory function. The special case where

(u) is the vector p-Laplacian

u

p-2u with p>1, is considered, and the applications deal with asymptotically positive homeogeneous nonlinearities and the Dirichlet problem for generalized Lienard systems.