Differentiation of Solutions of Boundary Value Problems with Respect to Nonlinear Boundary Conditions

We consider solutions of boundary value problems for the ordinary differential equation, y(n) = ƒ(x, y, y′, ..., y(n − 1), which satisfy gi(y(xi)) = yi, 1 ≤ i ≤ n, where x1 ≤ • • • ≤ xn and yi , 1 ≤ i ≤ n. The Implicit Function Theorem is used to establish results in which solutions of the boundary value problems are differentiated with respect to the boundary conditions.