TY - JOUR
T1 - About sign-constancy of Green's functions for impulsive second order delay equations
AU - Domoshnitsky, Alexander
AU - Landsman, Guy
AU - Yanetz, Shlomo
PY - 2014
Y1 - 2014
N2 - We consider the following second order differential equation with delay (Equation) In this paper we find necessary and sufficient conditions of positivity of Green's functions for this impulsive equation coupled with one or two-point boundary conditions in the form of theorems about differential inequalities. By choosing the test function in these theorems, we obtain simple sufficient conditions. For example, the inequality (Equation) is a basic one, implying negativity of Green's function of two-point problem for this impulsive equation in the case 0<γi≤1,0<δi≤1 for i = 1,..., p.
AB - We consider the following second order differential equation with delay (Equation) In this paper we find necessary and sufficient conditions of positivity of Green's functions for this impulsive equation coupled with one or two-point boundary conditions in the form of theorems about differential inequalities. By choosing the test function in these theorems, we obtain simple sufficient conditions. For example, the inequality (Equation) is a basic one, implying negativity of Green's function of two-point problem for this impulsive equation in the case 0<γi≤1,0<δi≤1 for i = 1,..., p.
KW - Boundary value problem
KW - Green's functions
KW - Impulsive equations
KW - Positivity/negativity of green's functions
KW - Second order
UR - http://www.scopus.com/inward/record.url?scp=84899574801&partnerID=8YFLogxK
U2 - 10.7494/OpMath.2014.34.2.339
DO - 10.7494/OpMath.2014.34.2.339
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AN - SCOPUS:84899574801
SN - 1232-9274
VL - 34
SP - 339
EP - 362
JO - Opuscula Mathematica
JF - Opuscula Mathematica
IS - 2
ER -