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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