# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Differentiability of solutions of second-order functional differential equations with unbounded delay. (English) Zbl 1027.34090
The authors study the differentiability of solutions to second-order functional-differential equations with unbounded delay, especially, when the phase space is reflexive or at least has the Radon-Nikodym property. The obtained results are then applied to linear equations to characterize the infinitesimal generator of solution semigroups associated with the linear equations under consideration.

##### MSC:
 34K30 Functional-differential equations in abstract spaces 34K05 General theory of functional-differential equations 34G10 Linear ODE in abstract spaces
##### Keywords:
asymptotic behaviour; continuous argument
Full Text:
##### References:
 [1] Butzer, P. L.; Berens, H.: Semi-groups of operators and approximation. (1967) · Zbl 0164.43702 [2] Diestel, J.; Uhl, J. J.: Vector measures. (1972) [3] Fattorini, H. O.: Second order linear differential equations in Banach spaces. (1985) · Zbl 0564.34063 [4] Goldstein, G. R.; Goldstein, J. A.: Regularity for semilinear abstract Cauchy problems. Lecture notes in pure and appl. Math. 178, 99-105 (1996) · Zbl 0858.34046 [5] Hale, J. K.; Lunel, S. M. Verduyn: Introduction to functional differential equations. (1993) · Zbl 0787.34002 [6] Hale, J. K.; Kato, J.: Phase space for retarded equations with infinite delay. Funkcial. ekvac. 21, 11-41 (1978) · Zbl 0383.34055 [7] Henrı\'quez, H. R.: Regularity of solutions of abstract retarded functional differential equations with unbounded delay. Nonlinear anal. 28, 513-531 (1997) · Zbl 0864.35112 [8] Henrı\'quez, H. R.: Periodic solutions of quasi-linear partial functional differential equations with unbounded delay. Funkcial. ekvac. 37, 329-343 (1994) · Zbl 0814.35141 [9] Henrı\'quez, H. R.; Vásquez, C. H.: Almost periodic solutions of abstract functional differential equations with unbounded delay. Acta appl. Math. 57, 105-132 (1999) · Zbl 0944.34058 [10] Henrı\'quez, H. R.; Vásquez, C. H.: Differentiability of solutions of the second order abstract Cauchy problem. Semigroup forum 64, 472-488 (2002) · Zbl 1032.47026 [11] Hino, Y.; Murakami, S.; Naito, T.: Functional differential equations with infinite delay. Lecture notes in math. 1473 (1991) · Zbl 0732.34051 [12] Marle, C. M.: Mesures et probabilités. (1974) · Zbl 0306.28001 [13] Kisyński, J.: On cosine operator functions and one-parameter groups of operators. Studia math. 49, 93-105 (1972) · Zbl 0232.47045 [14] Pazy, A.: Semigroups of linear operators and applications to partial differential equations. (1983) · Zbl 0516.47023 [15] Travis, C. C.; Webb, G. F.: Second order differential equations in Banach space. Proc. internat. Sympos. on nonlinear equations in abstract spaces, 331-361 (1987) [16] Travis, C. C.; Webb, G. F.: Compactness, regularity, and uniform continuity properties of strongly continuous cosine families. Houston J. Math. 3, 555-567 (1977) · Zbl 0386.47024 [17] Travis, C. C.; Webb, G. F.: Cosine families and abstract nonlinear second order differential equations. Acta math. Acad. sci. Hungar. 32, 76-96 (1978) · Zbl 0388.34039 [18] Wu, J.: Theory and applications of partial functional differential equations. (1996) · Zbl 0870.35116