Optimal interval lengths for nonlocal boundary value problems associated with third order Lipschitz equations |
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| Authors: | Stephen Clark Johnny Henderson |
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| Affiliation: | a Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, MI 65409-0020, USA
b Department of Mathematics, Baylor University, Waco, TX 76798-7328, USA |
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| Abstract: | For the third order differential equation, y?=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. |
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| Keywords: | Nonlinear boundary value problem Third order Lipschitz equation Nonlocal boundary condition Existence Uniqueness Optimal control |
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