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Proceedings of the American Mathematical Society

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

 

 

Asymptotics of differential systems with deviating arguments


Author: William F. Trench
Journal: Proc. Amer. Math. Soc. 92 (1984), 219-224
MSC: Primary 34K25
MathSciNet review: 754707
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Abstract: Conditions are given which imply that a system $ X'(t) = F[t,X(g(t))]$ has a solution with some components which approach given limits with specified orders of convergence as $ t \to \infty $, while the other components have specified orders of magnitude. The integral smallness conditions on $ F$ permit conditional convergence of some of the improper integrals that occur, and it is not required that $ {\lim _{t \to \infty }}g(t) = \infty $.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0754707-8
Article copyright: © Copyright 1984 American Mathematical Society