**Alexander Domoshnitsky, Michael Drakhlin, and Elena Litsyn**

## On Boundary Value Problems for *n*-th Order Functional Differential Equations with Impulses

**abstract:**

A boundary value problem is considered for an $N$-th order functional
differential equation with impulses. It is reduced to the same boundary value
problem for another equation of the same order without impulses. The reduction
is based on constructing of an isomorphism between the space of the functions
which are piecewise absolutely continuous up to the $(N\!-\!1)$-st derivative and
satisfy the impulse conditions, at the discontinuity points and the space of
the functions which are absolutely continuous up to the $(N\!-\!1)$-st derivative.
The approach allows to derive conditions on the sign preservation for the
Green function of the considered boundary value problem.

**Mathematics Subject Classification:**
34K10.

**Key words and phrases:**
Functional differential equation, boundary value
problem, isomorphism, Green operator.