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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:
34K30Functional-differential equations in abstract spaces
34K05General theory of functional-differential equations
34G10Linear ODE in abstract spaces
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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