Title

Optimal Interval Lengths for Nonlocal Boundary Value Problems Associated with Third Order Lipschitz Equations

Abstract

For the third order differential equation, y triple prime=f(x,y,y′,y″), where f(x,y1,y2,y3) is Lipschitz continuous in terms of yi, i=1,2,3, we obtain optimal bounds on the length of intervals on which there exist unique solutions of certain nonlocal three and four point boundary value problems. These bounds are obtained through an application of the Pontryagin Maximum Principle from the theory of optimal control.

Department(s)

Mathematics and Statistics

Sponsor(s)

National Science Foundation (U.S.)

Keywords and Phrases

existence; nonlinear boundary value problem; nonlocal boundary condition; optimal control; third order Lipschitz equation; uniqueness

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2006 Elsevier, All rights reserved.

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