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Zbl 0858.34055
Pseudo almost periodic solutions of some delay differential equations.
(English)
[J] J. Math. Anal. Appl. 201, No.3, 840-850 (1996). ISSN 0022-247X

The theory of exponential dichotomy is used successfully to establish the existence of pseudo almost periodic solutions of delay-differential equations of the form $x'(t)=L(t)x_t+f(t)$, $t\ge \sigma$, $x_\sigma=\varphi$, where $(\sigma,\varphi)\in\bbfR\times C([-r,0],\bbfR^n)$, $r>0$, which have pseudo almost periodic coefficients. Also the following theorem is proved: If $\sigma(A)\cap i\bbfR=\phi$ and $f:\bbfR\to\bbfR^n$ is continuous and pseudo almost periodic, where $\sigma(A)$ is the spectrum of the infinitesimal generator $A$, then $x'(t)=Lx_t+f(t)$ has a unique bounded solution which is also pseudo almost periodic.
[N.Parhi (Berhampur)]
MSC 2000:
*34K14 Almost periodic solutions of functional differential equations
34C27 Almost periodic solutions of ODE

Keywords: exponential dichotomy; pseudo almost periodic solutions; delay-differential equations

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