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Zbl 1217.34113
Cheng, Rong
Oscillatory periodic solutions for two differential-difference equations arising in applications. (English)
[J] Abstr. Appl. Anal. 2011, Article ID 635926, 12 p. (2011). ISSN 1085-3375; ISSN 1687-0409/e

Summary: We study the existence of oscillatory periodic solutions for two nonautonomous differential-difference equations (which arise in a variety of applications) of the following form: $$\dot x(t)=-f(t,x(t-r))$$ and $$\dot x(t)=-f(t,x(t-s))-f(t,x(t-2s),$$ where $f\in C(\Bbb R\times\Bbb R,\Bbb R)$ is odd with respect to $x$, and $r,s>0$ are two given constants. By using a symplectic transformation and a result for Hamiltonian systems, the existence of oscillatory periodic solutions of the above-mentioned equations is established.

MSC 2000:: *34K13 Periodic solutions of functional differential equations

Keywords: oscillatory periodic solutions; two nonautonomous differential-difference equations; symplectic transformation; Hamiltonian systems

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