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Proceedings of the American Mathematical Society

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

 

 

Systems of differential equations subject to mild integral conditions


Author: William F. Trench
Journal: Proc. Amer. Math. Soc. 87 (1983), 263-270
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9939-1983-0681832-1
MathSciNet review: 681832
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Abstract: It is shown that solutions of a system $ x' = f(t,x)$ approach constant vectors as $ t \to \infty $, under assumptions which do not require that $ \vert\vert {f(t,x)} \vert\vert \leqslant w(t,\vert\vert x \vert\vert)$, where $ w$ is nondecreasing in $ \vert\vert x \vert\vert$, and which permit some or all of the integral smallness conditions on $ f$ to be stated in terms of ordinary--rather than absolute--convergence. Estimates of the order of convergence are given.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0681832-1
Article copyright: © Copyright 1983 American Mathematical Society