About sign-constancy of Green's function of a two-point problem for impulsive second order delay equations

We consider the following second order differential equation with delay (Lx) (t) x `'(t) + Sigma(p)(j=1) a(j)(t)x'(t - tau(j) (t)) + Sigma(p)(j=1) b(j)(t)x(t - theta(j)(t)) = f(t), t is an element of [0, omega] x(t(k)) = gamma(k)x(t(k) - 0), x'(t(k)) = delta(k)x'(t(k) - 0), k = 1, 2, ..., r. In this paper we find sufficient conditions of positivity of Green's functions for this impulsive equation coupled with two-point boundary conditions in the form of theorems about differential inequalities..