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Zbl 0796.34029
Zhang, Chuanyi
Pseudo almost periodic solutions of some differential equations.
(English)
[J] J. Math. Anal. Appl. 181, No.1, 62-76 (1994). ISSN 0022-247X

The concept of a pseudo almost periodic function on $R$ or $\Omega\times R$, $R\subset C\sp n$, generalizes the concept of an almost periodic (in sense of Bohr) function. A bounded on $R$ $(\Omega\times R)$ function is said to be pseudo almost periodic if $f= g+ \varphi$, where $g$ is almost periodic on $R$ $(\Omega\times R)$ and $\varphi$ satisfies the condition $$\lim\sb{t\to\infty} {1\over 2t}\int\sb{-t}\sp t\vert\varphi(x)\vert dx=0,$$ $$\left(\lim\sb{t\to\infty}{1\over 2t}\int\sb{-t}\sp t \vert\varphi(z,x)\vert dx=0\quad\text{uniformly in }z\in\Omega\right).$$ The purpose of the paper is to establish existence of pseudo almost periodic solutions of linear and quasi-linear ordinary and parabolic partial differential equations. The following proposition is an emanation of the paper spirit:\par Consider the system of the form ${dY\over dx}= AY+ F$, where $A$ is a complex $n\times n$ matrix of $F: R\to R\sp n$ is a vector function, whose components are pseudo almost periodic. If the matrix $A= (a\sb{ij})$ has no eigenvalues with real part zero, then this system admits a unique solution $Y$, whose components are pseudo almost periodic.
[I.Ginchev (Varna)]
MSC 2000:
*34C27 Almost periodic solutions of ODE

Keywords: existence of pseudo almost periodic solutions; linear and quasi-linear ordinary and parabolic partial differential equations

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