TY - JOUR

T1 - About sign-constancy of Green's function of a two-point problem for impulsive second order delay equations

AU - Domoshnitsky, Alexander

AU - Landsman, Guy

AU - Yanetz, Shlomo

N1 - 10th Colloquium on the Qualitative Theory of Differential Equations, Szeged, HUNGARY, JUL 01-04, 2015

PY - 2016

Y1 - 2016

N2 - 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..

AB - 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..

KW - impulsive equations

KW - Green's functions

KW - positivity/negativity of Green's functions

KW - boundary value problem

KW - second order

U2 - 10.14232/ejqtde.2016.8.9

DO - 10.14232/ejqtde.2016.8.9

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SN - 1417-3875

JO - Electronic Journal of Qualitative Theory of Differential Equations

JF - Electronic Journal of Qualitative Theory of Differential Equations

ER -