Differentiability of solutions of linear functional differential equations with infinite delay

Authors

  • Hernán R. Henríquez Miranda Universidad de Santiago.

DOI:

https://doi.org/10.4067/S0716-09172002000200004

Keywords:

Abstract retarded functional differential equations, semigroups of linear operators, differentiability of solutions, ecuaciones diferenciales funcionales retardadas y abstractas, semigrupos de operadores lineales, diferenciabilidad de soluciones.

Abstract

In this note we establish a criterion to obtain classical solutions for a quasi-linear abstract retarded functional differential equation with infinite delay and we apply this result to characterize the infinitesimal generators of several strongly continuous semigroup of linear operators that arise in the theory of linear abstract retarded functional differential equations with infinite delay on a phase space defined axiomatically.

Author Biography

Hernán R. Henríquez Miranda, Universidad de Santiago.

Departamento de Matemática.

References

[1] P. L. Butzer and H. Berens, Semi-Groups of Operators and Approximation. Springer-Verlag, Berlin, (1967).

[2] J. Diestel and J. J. Uhl, Vector Measures. Amer. Math. Society, (1972).

[3] Engel, K-J. and R. Nagel, One-parameter Semigroups for Linear Evolution Equations. Springer-Verlag, New York, (2000).

[4] G. R. Goldstein and J. A. Goldstein, Regularity for Semilinear Abstract Cauchy Problems. Lect. Notes in Pure and Applied Maths. 178. Marcel Dekker, New York, pp. 99-105, (1996).

[5] J. K. Hale and J. Kato, Phase Space for Retarded Equations with Infinite Delay, Funkcial. Ekvac. 21, pp. 11-41, (1978).

[6] H. R. Henríquez, Regularity of Solutions of Abstract Retarded Functional Differential Equations with Unbounded Delay. Nonlinear Analysis, Theory, Methods & Applications 28 (3), pp. 513-531, (1997).

[7] H. R. Henríquez, Periodic Solutions of Quasi-Linear Partial Functional Differential Equations with Unbounded Delay. Funkcialaj Ekvac. 37 (2), pp. 329-343, (1994).

[8] Henr´?quez, H. R., Approximation of Abstract Functional Differential Equations with Unbounded Delay, Indian J. Pure and Applied Maths. 27 (4), pp. 357-386, (1996).

[9] Y. Hino, S. Murakami and T. Naito, Functional Differential Equations with Infinite Delay. Lect. Notes in Maths. 1473. SpringerVerlag, Berlin, (1991).

[10] C. M. Marle, Mesures et Probabilit´es. Hermann, Paris, (1974).

[11] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York, (1983).

[12] W. Ruess, Existence and Stability of Solutions to Partial Functional Differential Equations with Delay. Adv. Diff. Eqns. 4 (6), pp. 843-876, (1999).

[13] W. Ruess, Existence of Solutions to Partial Functional Differential Equations with Delay. in A. G. Kartsatos (ed), Theory and Applications of Nonliner Operators of accretive and Monotone Type. Lect. Notes in Pure and Applied Maths. 178, M. Dekker, New York, 1996, pp.259-288.

[14] C. C. Travis and G. F. Webb, Existence and Stability for Partial Functional Differential Equations, Trans. Amer. Math. Soc. 200, pp. 395-418, (1974).

Published

2002-06-01

How to Cite

[1]
H. R. Henríquez Miranda, “Differentiability of solutions of linear functional differential equations with infinite delay”, Proyecciones (Antofagasta, On line), vol. 21, no. 2, pp. 155-174, Jun. 2002.

Issue

Section

Artículos