Existence and uniqueness of solutions to two point boundary value problems for ordinary differential equations

摘要

In this paper, using the optimal control method, we deal with the following boundary value problem yn+f(x,y)=0, y(0)=c, y(1)=d, under new nonresonance conditions of the form -A≤f'y(x,y)≤β(x)≤B, where A>0. We obtain the existence and uniqueness of solutions of the BVP (1).