On existence and uniqueness of solutions for ordinary differential equations with nonlinear boundary conditions.

We prove an existence and uniqueness theorem for a nonlinear functional boundary value problem, that is, an ordinary differential equation with a nonlinear boundary condition. The proof is based on a Global Inversion Theorem of Ambrosetti and Prodi, which is applied to the boundary operator restricted to the manifold of the global solutions to the equation. Our result is a generalization of an analogous existence and uniqueness theorem of G. Vidossich, as it is shown with some examples.