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MATHEMATICA BOHEMICA, Vol. 126, No. 1, pp. 221-228 (2001)
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# Partially irregular almost periodic solutions of ordinary differential systems

## Alexandr Demenchuk

* Alexandr Demenchuk*, Department of Differential Equations, Institute of Mathematics, National Academy of Sciences of Belarus, Surganova 11, 220072 Minsk, Belarus, e-mail: ` demenchuk@im.bas-net.by`

**Abstract:**
Let $f(t,x)$ be a vector valued function almost periodic in $t$ uniformly for $x$, and let $ mod(f)=L_1\oplus L_2$ be its frequency module. We say that an almost periodic solution $x(t)$ of the system $$ \dot x = f (t, x), \quad t\in \R , x\in D \subset \R ^n $$ is irregular with respect to $L_2$ (or partially irregular) if $( mod(x)+L_1) \cap L_2 = \{0\}$. \endgraf Suppose that $ f(t,x) = A(t)x + X(t, x), $ where $A(t)$ is an almost periodic $(n\times n)$-matrix and $ mod (A)\cap mod(X)= \{0\}.$ We consider the existence problem for almost periodic irregular with respect to $ mod (A)$ solutions of such system. This problem is reduced to a similar problem for a system of smaller dimension, and sufficient conditions for existence of such solutions are obtained.

**Keywords:** almost periodic differential systems, almost periodic solutions

**Classification (MSC2000):** 34C27

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