Solutions of multipoint boundary value problems for second order equations

Shooting methods are employed to obtain solutions of the second order differential equation, y" = f(x,y,y'), satisfying the multipoint nonlocal boundary conditions, y(x(0)) = y(1), y(x(n+1)) - Sigma(i=1)(n) y(x(i)) = y(2), a < x(0) < x(1) < (...) < x(n+1) < b, and y(1), y(2) is an element of R, where f: (a, b) x R-2 -> R is continuous. It is assumed that solutions of such problems are unique, when they exist.