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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

✍ Scribed by Paul Eloe; Johnny Henderson

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
131 KB
Volume
284
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

For the __n__th 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 − j~0~; j~0~)‐point unique solvability implies (k; j)‐point unique solvability for 1 ⩽ j ⩽ j~0~, and 1 ⩽ k ⩽ n − j. This result is in analogy to n‐point disconjugacy implies k‐point disconjugacy, 2 ⩽ k ⩽ n − 1. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim

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