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Proceedings of the American Mathematical Society

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



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
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 \[ (d/dt)[x(t) - b(t)x(t - r)] = F[t,x(t),x(t - r)]\] 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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Keywords: Asymptotic periodicity, neutral equations, monotone systems
Article copyright: © Copyright 1991 American Mathematical Society