**Robert Hakl, Sulkhan Mukhigulashvili**

## On a Boundary Value Problem
for *n*-th Order Linear Functional Differential Systems

**Abstract:**

In this paper, theorems on the Fredholm alternative and well-posedness of the
linear boundary value problem

$$u'(t)=\ell(u)(t)+q(t),\quad h(u)=c,$$

where $\ell:C([a,b];R^n)\to L([a,b];R^n$ and $h:\cabrn\to R^n$ are linear
bounded operators, $q\inL([a,b];R^n$, and $c\in R^n$, are established even when
$\ell$ is not a strongly bounded operator.

**Keywords:**

Fredholm alternative, well-posedness, functional differential systems, $n$-th
order linear boundary value problem.

**MSC 2000:** 34K06, 34K10