Nonlinear boundary value problems for ordinary differential equations (Q1331009)

A nonlinear vector boundary value problem of the form (1) \(y'= f(x,y)\), (2) \(B(y)= r\) is considered. Results are presented in which it is shown that solutions \(u(x)\) of (1), (2) can be differentiated with respect to the components of \(r\). These partial derivatives are then shown to be solutions of certain linear boundary value problems. These results can be considered as analogues of well-known results for differentiability of solutions of (1) with respect to initial conditions.