OPTIMAL INTERVAL LENGTHS FOR NONLOCAL BOUNDARY VALUE PROBLEMS FOR SECOND ORDER LIPSCHITZ EQUATIONS

摘要

For the second order differential equation, y" = f(t,y,y'), where f(t,ri,r2) is Lipschit/ eontinnous in terms of r and r_2, we obtain optimal bounds on the length of intervals on which there exisl unique solutions of 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.