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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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Asymptotic periodicity of solutions to a class of neutral functional-differential equations
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by Jian Hong Wu PDF
Proc. Amer. Math. Soc. 113 (1991), 355-363 Request permission

Abstract:

In this paper, we extend a convergence result due to Takáč to continuous maps satisfying certain monotonicity properties. Applying this extension to the Poincaré map associated with the neutral equation \[ (d/dt)[x(t) - b(t)x(t - r)] = F[t,x(t),x(t - r)]\] we prove that each solution of the above neutral equation tends to an $r$-periodic function as $t \to \infty$ in an oscillatory manner, where $0 \leq b(t) < 1$ is an $r$-periodic continuous function and $F$ satisfies a certain order relation.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 113 (1991), 355-363
  • MSC: Primary 34K15; Secondary 34K20
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1079900-2
  • MathSciNet review: 1079900