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

Johnny Henderson

doi:10.26637/mjm0101/004

Abstract

For the \(n\)th order differential equation, \(y^{(n)}=f\left(t, y, y^{\prime}, \ldots, y^{(n-1)}\right)\), where \(f\left(t, r_1, r_2, \ldots, r_n\right)\) 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

Mathematics Subject Classification:

34B15, 49J15

Authors Imprint References Funding Related Articles Downloads

Johnny Henderson Department of Mathematics, Baylor University, Waco, Texas 76798-7328, USA. https://orcid.org/0000-0001-7288-5168

Pages: 19-25
Date Published: 01-09-2012
Vol. 1 No. 1 (2012): Inaugural Issue :: Malaya Journal of Matematik (MJM)

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