**R. Hakl, A. Lomtatidze, and J. \v Sremr**

## On constant sign solutions
of a periodic type boundary
value problems for first order
functional differential equations

**abstract:**

In this paper the question on the existence and uniqueness of a constant sign
solution of a periodic type boundary value problem
is studied. More precisely, the nonimprovable
effective sufficient conditions for a linear bounded operator
$\ell:\cabr\to\labr$ are established guaranteeing that the problem
$$
u'(t)=\ell(u)(t)+q(t),\qquad u(a)-\lambda u(b)=c,
$$
where $q\in\labrp$, $\lambda$ $\in\rp$, has a unique solution, and this
solution does not change its sign.

**Mathematics Subject Classification:**
34K06, 34K10.

**Key words and phrases:**
Linear functional
differential equation, periodic type boundary value problem,
solvability and unique solvability.