TY - JOUR
T1 - On Oscillation of a Second Order Impulsive Linear Delay Differential Equation
AU - Berezansky, L.
AU - Braverman, E.
N1 - Funding Information:
Acknowledgement This work was undertaken as an activity within the project ``Prevention of muscular disorders in operation of computer input devices (PROCID)'', a Concerted Action financed under the European Union research programme BIOMED-2 (BMH-98-3903).
PY - 1999/5/1
Y1 - 1999/5/1
N2 - For the delay differential equationẍt+∑k=1maktxgkt=0, gkt≤t,with impulsive conditionsxτj=Ajxτj-0,ẋτ j=Bjẋτj-0,a connection between the following properties is established: nonoscillation of the differential equation and the corresponding differential inequality, positiveness of the fundamental function and the existence of a solution of a generalized Riccati inequality. Explicit conditions for nonoscillation and oscillation and comparison theorems are presented.
AB - For the delay differential equationẍt+∑k=1maktxgkt=0, gkt≤t,with impulsive conditionsxτj=Ajxτj-0,ẋτ j=Bjẋτj-0,a connection between the following properties is established: nonoscillation of the differential equation and the corresponding differential inequality, positiveness of the fundamental function and the existence of a solution of a generalized Riccati inequality. Explicit conditions for nonoscillation and oscillation and comparison theorems are presented.
UR - https://www.scopus.com/pages/publications/0001045025
U2 - 10.1006/jmaa.1999.6297
DO - 10.1006/jmaa.1999.6297
M3 - Article
AN - SCOPUS:0001045025
SN - 0022-247X
VL - 233
SP - 276
EP - 300
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -