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Zbl 1205.34084
Wang, Zhengxin; Qian, Longxia; Lu, Shiping; Cao, Jinde
The existence and uniqueness of periodic solutions for a kind of Duffing-type equation with two deviating arguments.
(English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 9, 3034-3043 (2010). ISSN 0362-546X

The Duffing-type delay differential equation $$x''(t) + f(x(t-\tau(t))) + g(x(t-\gamma(t))) = e(t)$$ is considered, where $\tau$, $\gamma$ and $e$ are real-valued continuous periodic functions with period $T$, $\tau'(t) <1$, $\gamma'(t) < 1$, $\int^T_0e(t)\,dt = 0$, and $f$ and $g$ are $C^1$ functions satisfying $f(c) + g(c) \not\equiv e(t)$ for all $t$ and $c$. Sufficient conditions are provided to ensure the existence, as well as uniqueness, of $T$-periodic solutions and it is claimed that these complement some known results.
[Zhanyuan Hou (London)]
MSC 2000:
*34K13 Periodic solutions of functional differential equations

Keywords: periodic solutions; Duffing equations; deviating arguments

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