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Asymptotic periodicity of solutions to a class of neutral functional-differential equations


Author: Jian Hong Wu
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
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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

$\displaystyle (d/dt)[x(t) - b(t)x(t - r)] = F[t,x(t),x(t - r)]$

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

DOI: https://doi.org/10.1090/S0002-9939-1991-1079900-2
Keywords: Asymptotic periodicity, neutral equations, monotone systems
Article copyright: © Copyright 1991 American Mathematical Society

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