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

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- by Jian Hong Wu
- Proc. Amer. Math. Soc.
**113**(1991), 355-363 - DOI: https://doi.org/10.1090/S0002-9939-1991-1079900-2
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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 \[ (d/dt)[x(t) - b(t)x(t - r)] = F[t,x(t),x(t - r)]\] 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.## References

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## Bibliographic 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