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28th Southeastern-Atlantic Regional Conference on Differential Equations
October 10-11, 2008
University of Arkansas at Little Rock
Little Rock Arkansas, USA

Organizers
Eric R. Kaufmann, Nickolai Kosmatov

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Uniqueness Implies Existence and Uniqueness Conditions for a Class of (k+j)-Point Boundary Value Problems for nth Order Differential Equations
by
Paul Eloe
University of Dayton
Coauthors: Johnny Henderson, Baylor University

For the nth order nonlinear differential equation, y(n) = f(x, y, y', ..., y(n-1)), we consider uniqueness implies existence results for solutions satisfying certain (k+j)-point boundary conditions, 1 ≤ j ≤ n-1, and 1 ≤ k ≤ n-j. We define (k;j)-point unique solvability in analogy to k-point disconjugacy and we show that (n-j0;j0)-point unique solvability implies (k;j)-point unique solvability for 1 ≤ j ≤ j0, and 1 ≤ k ≤ n-j. This result is in analogy to n-point disconjugacy implies k-point disconjugacy, 2 ≤ k ≤ n-1.

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Date received: August 22, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caww-10.