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