Abstract:

We consider a linear  system of differential equations $x'=a(t)x-\mu x$  with a conditionally periodic matrix $a$ and a parameter $\mu\in\mathbb C$. We prove that there exists  a nonempty set $M\subset\mathbb C$ such that for each $\mu\in M $ the spatial periodic extension of this system, which is a system of first order partial differential equations, has a generalized (in the framework of Schwartz's theory of distributions) periodic solution.