Uniqueness implies existence of solutions for nonlinear focal-like boundary value problems

Given an appropriate growth condition for ff and a uniqueness assumption on y(n)=0y(n)=0 with respect to certain focal boundary value problems, it is shown that uniqueness of solutions to the nonlinear differential equation y(n)=f(t,y,y′,…,y(n−1)),y(n)=f(t,y,y′,…,y(n−1)), subject to boundary conditions of the form gij(y(tj),…,y(n−1)(tj))=yijgij(y(tj),…,y(n−1)(tj))=yij implies existence of solutions.