Abstract: We study the nonlinear boundary value problem:
ey"=f(x,e,y,y'),y(0,e)=A(e),y(1,e)=B(e)
where e>0 is a small parameter, y, f, A and B are n-dimensional vector functions. This vector nonlinear bundary value problem does not appear to have been studied, although the scalar boundary value problem has been treated extensively. Under appropriate assumptions, using method of differential inequality we can find a solution and estimate it as well.