Alexander Domoshnitsky, Michael Drakhlin, and Elena Litsyn

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

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.