TY - JOUR
T1 - Differentiability of solutions of second-order functional differential equations with unbounded delay
AU - Henríquez, Hernán R.
AU - Vásquez, Carlos H.
N1 - Funding Information:
This work was supported by DICYT-USACH, Project 04-9633HM and FONDECYT, Project 1970716. Corresponding author. E-mail addresses: hhenriqu@lauca.usach.cl (H.R. Henríquez), cvasquez@impa.br (C.H. Vásquez).
PY - 2003/4/15
Y1 - 2003/4/15
N2 - In this paper we study the differentiability of solutions of the second-order semilinear abstract retarded functional differential equation with unbounded delay, specially when the underlying space is reflexive or at least has the Radon-Nikodym property. We apply our results to characterize the infinitesimal generators of several strongly continuous semigroups of linear operators that arise in the theory of linear abstract retarded functional differential equations with unbounded delay on a phase space defined axiomatically.
AB - In this paper we study the differentiability of solutions of the second-order semilinear abstract retarded functional differential equation with unbounded delay, specially when the underlying space is reflexive or at least has the Radon-Nikodym property. We apply our results to characterize the infinitesimal generators of several strongly continuous semigroups of linear operators that arise in the theory of linear abstract retarded functional differential equations with unbounded delay on a phase space defined axiomatically.
KW - Abstract Cauchy problem
KW - Cosine functions of operators
KW - Differentiability of solutions
KW - Functional differential equations
UR - http://www.scopus.com/inward/record.url?scp=0038730525&partnerID=8YFLogxK
U2 - 10.1016/S0022-247X(03)00042-8
DO - 10.1016/S0022-247X(03)00042-8
M3 - Article
AN - SCOPUS:0038730525
SN - 0022-247X
VL - 280
SP - 284
EP - 312
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -