TY - JOUR
T1 - Stability of abstract nonlinear nonautonomous differential-delay equations with unbounded history-responsive operators
AU - Gil', M. I.
N1 - Funding Information:
✩ This research was supported by the Kamea Fund of the Israel. E-mail address: [email protected].
PY - 2005/8/1
Y1 - 2005/8/1
N2 - We consider a class of nonautonomous functional-differential equations in a Banach space with unbounded nonlinear history-responsive operators, which have the local Lipshitz property. Conditions for the boundedness of solutions, Lyapunov stability, absolute stability and input-output one are established. Our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators.
AB - We consider a class of nonautonomous functional-differential equations in a Banach space with unbounded nonlinear history-responsive operators, which have the local Lipshitz property. Conditions for the boundedness of solutions, Lyapunov stability, absolute stability and input-output one are established. Our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators.
KW - Absolute stability
KW - Abstract nonlinear differential-delay equations
KW - Boundedness of solutions
KW - Input-output stability
KW - Lyapunov stability
UR - http://www.scopus.com/inward/record.url?scp=19044397052&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2004.11.018
DO - 10.1016/j.jmaa.2004.11.018
M3 - Article
AN - SCOPUS:19044397052
SN - 0022-247X
VL - 308
SP - 140
EP - 158
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -