Optimal intervals for uniqueness of solutions for lipschitz nonlocal boundary value problems

Johnny Hendersona,*

Optimal intervals for uniqueness of solutions for lipschitz nonlocal boundary value problems

Authors :

Johnny Henderson^a,*

Author Address :

^aDepartment of Mathematics, Baylor University, Waco, Texas 76798-7328, USA.

*Corresponding author.

Abstract :

For the $n$th order differential equation, $y^{(n)} = f(t, y, y’, \ldots, y^{(n-1)})$, where $f(t, r_1, r_2,$ $ \ldots,r_n)$ satisfies a Lipschitz condition in terms of $r_i, 1 \leq i \leq n$, 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.

Keywords :

Nonlocal boundary value problem, optimal length intervals, Pontryagin maximum principle.

DOI :

Article Info :

Received : August 24, 2012; Accepted : September 05, 2012.