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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Asymptotics of differential systems with deviating arguments
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by William F. Trench PDF
Proc. Amer. Math. Soc. 92 (1984), 219-224 Request permission

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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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 92 (1984), 219-224
  • MSC: Primary 34K25
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0754707-8
  • MathSciNet review: 754707