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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A compactness condition for solutions of ordinary differential equations


Author: L. K. Jackson
Journal: Proc. Amer. Math. Soc. 57 (1976), 89-92
MSC: Primary 34B15
DOI: https://doi.org/10.1090/S0002-9939-1976-0404743-1
MathSciNet review: 0404743
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Abstract: It is proven that a sequence $ \{ {y_k}(x)\} $ of solutions of $ {y^{(n)}} = f(x,y,y', \ldots ,{y^{(n - 1)}})$ with $ \{ {y_k}(x)\} $ uniformly bounded on a compact interval $ [c,d]$ has a bounded total variation sequence $ \{ V_c^d({y_k})\} $ provided solutions of the differential equation extend and $ n$-point boundary value problems have at most one solution.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0404743-1
Keywords: Boundary value problem, total variation, Kamke Convergence Theorem, Green's function, Schauder-Tychonoff Theorem
Article copyright: © Copyright 1976 American Mathematical Society