TY - JOUR
T1 - On oscillation properties of delay differential equations with positive and negative coefficients
AU - Berezansky, Leonid
AU - Domshlak, Yury
AU - Braverman, Elena
N1 - Funding Information:
The first and the third author were partially supported by Israel Ministry of Absorption.
PY - 2002/10/1
Y1 - 2002/10/1
N2 - For a scalar delay differential equation x(t) + a(t)x(h(t)) - b(t)x(g(t)) = 0, a(t) ≥ 0, b(t) ≥ 0, h(t) ≤ t, g(t) ≤ t, a connection between the following properties is established: nonoscillation of the differential equation and the corresponding differential inequalities, positiveness of the fundamental function and existence of a nonnegative solution for a certain explicitly constructed nonlinear integral inequality. A comparison theorem and explicit nonoscillation and oscillation results are presented.
AB - For a scalar delay differential equation x(t) + a(t)x(h(t)) - b(t)x(g(t)) = 0, a(t) ≥ 0, b(t) ≥ 0, h(t) ≤ t, g(t) ≤ t, a connection between the following properties is established: nonoscillation of the differential equation and the corresponding differential inequalities, positiveness of the fundamental function and existence of a nonnegative solution for a certain explicitly constructed nonlinear integral inequality. A comparison theorem and explicit nonoscillation and oscillation results are presented.
UR - http://www.scopus.com/inward/record.url?scp=0036814928&partnerID=8YFLogxK
U2 - 10.1016/S0022-247X(02)00246-9
DO - 10.1016/S0022-247X(02)00246-9
M3 - Article
AN - SCOPUS:0036814928
SN - 0022-247X
VL - 274
SP - 81
EP - 101
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -