If $Y$ is a subset of the space ${ℝ}^n\times {ℝ}^n$, we call a pair of continuous functions $U$, $V$$Y$-compatible, if they map the space ${ℝ}^n$ into itself and satisfy $Ux·Vy\ge 0$, for all $(x,y)\in Y$ with $x·y\ge 0$. (Dot denotes inner product.) In this paper a nonlinear two point boundary value problem for a second order ordinary differential $n$-dimensional system is investigated, provided the boundary conditions are given via...