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Zbl 1118.34063
Wu, Jun; Wang, Zhicheng
Two periodic solutions of second-order neutral functional differential equations.
(English)
[J] J. Math. Anal. Appl. 329, No. 1, 677-689 (2007). ISSN 0022-247X

The authors investigate the existence, multiplicity and nonexistence of positive periodic solutions for the following second-order neutral functional differential equations $$(x(t)-cx(t-\delta))''+a(t)x(t)=\lambda b(t)f(x(t-\tau(t))),$$ where $\lambda$ is a positive parameter, $c$ and $\delta$ are constants and $\vert c\vert \not=1$. The criteria essentially depend on the limits of the function $f(u)/u$ as $u$ tends to zero or infinity. The approach is based on the Krasnoselskii fixed point theorem.
[Meng Fan (Changchun)]
MSC 2000:
*34K13 Periodic solutions of functional differential equations
34K40 Neutral equations
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: Krasnoselskii fixed point theorem

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