Communications on Applied Nonlinear Analysis
For the nth order differential equation (see PDF for equation) we obtain optimal bounds on the length of intervals on which solutions are unique for certain nonlocal three point boundary value problems. These bounds are obtained through an application of the Pontryagin Maximum Principle from the theory of optimal control.
Eloe, Paul W. and Henderson, Johnny, "Optimal intervals for uniqueness of solutions for nonlocal boundary value problems" (2011). Mathematics Faculty Publications. 127.