TY - JOUR
T1 - Negativity of Green’s Functions to Focal and Two-Point Boundary Value Problems for Equations of Second Order with Delay and Impulses in Their Derivatives
AU - Domoshnitsky, Alexander
AU - Malev, Sergey
AU - Raichik, Vladimir
N1 - Publisher Copyright:
© 2022 by the authors.
PY - 2022/10
Y1 - 2022/10
N2 - We consider the second-order impulsive differential equation with impulses in derivative and without the damping term. Sufficient conditions that a nontrivial solution of the homogeneous equation having a zero of its derivative does not have a zero itself are obtained. On the basis of the obtained results on differential inequalities, which can be considered as analogues of the Vallee–Poussin theorems, new sufficient conditions on the negativity of Green’s functions are obtained.
AB - We consider the second-order impulsive differential equation with impulses in derivative and without the damping term. Sufficient conditions that a nontrivial solution of the homogeneous equation having a zero of its derivative does not have a zero itself are obtained. On the basis of the obtained results on differential inequalities, which can be considered as analogues of the Vallee–Poussin theorems, new sufficient conditions on the negativity of Green’s functions are obtained.
KW - focal intervals
KW - Green’s function
KW - positivity of solutions
KW - second-order impulsive differential equations
KW - semi-nonoscillation intervals
KW - Vallee–Poussin theorem on differential inequality for impulsive equations
UR - http://www.scopus.com/inward/record.url?scp=85139754073&partnerID=8YFLogxK
U2 - 10.3390/math10193683
DO - 10.3390/math10193683
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AN - SCOPUS:85139754073
SN - 2227-7390
VL - 10
JO - Mathematics
JF - Mathematics
IS - 19
M1 - 3683
ER -