Systems of differential equations with fully nonlinear boundary conditions

We give sufficient conditions involving f, g and Omega in order that systems of differential equations of the form y '' = f(x,y,y'), z in [0, 1] with fully nonlinear boundary conditions of the form g((y(0), y(1)), (y'(0), y'(1))) = 0 have solutions y with (z,y) in <(Omega)over bar> subset of or equal to [0,1] x R-n. We use Schauder degree theory in a novel space. Well known existence results for the Picard, the periodic and the Neumann boundary conditions follow as special cases of our results.