Optimal Intervals for Uniqueness of Solutions for Nonlocal Boundary Value Problems

摘要

For the nth order differential equation, y~(n) = f(t,y,y',...,y~(n-1)), where f(t, T_1, T_2, ..., r_n) is Lipschitz continuous in terms of n, 1 ≤ i ≤ n, 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.