Optimal Interval Lengths for Nonlocal Boundary Value Problems Associated with Third Order Lipschitz Equations
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.
S. L. Clark and J. Henderson, "Optimal Interval Lengths for Nonlocal Boundary Value Problems Associated with Third Order Lipschitz Equations," Journal of Mathematical Analysis and Applications, Elsevier, Jan 2006.
The definitive version is available at https://doi.org/10.1016/j.jmaa.2005.09.017
Mathematics and Statistics
National Science Foundation (U.S.)
Keywords and Phrases
existence; nonlinear boundary value problem; nonlocal boundary condition; optimal control; third order Lipschitz equation; uniqueness
Article - Journal
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