Regularity of solutions of partial neutral functional differential equations with unbounded delay
DOI:
https://doi.org/10.4067/S0716-09172002000100005Keywords:
Retarded functional differential equations, abstract Cauchy problem, semigroup of bounded linear operators, regularity of solutions, ecuaciones diferenciales funcionales con retardo, problema abstracto de Cauchy, semigrupos de operadores lineales acotadosAbstract
We prove the existence of regular solutions for a class of quasi-linear partial neutral functional differential equations with unbounded delay that can be described as the abstract retarded functional differential equation
(x(t) + F (t,x?)) = Ax(t)+G(t,x?), where A is the infinitesimal generator of a strongly continuous semigroup of bounded linear operators on a Banach space X and F , G are appropriated functions.
References
[1] Goldstein, Jerome A. Semigroups of linear operators and applications. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, (1985).
[2] Hale, Jack K.; Kato, Junji.(1978) Phase space for retarded equations with infinite delay. Funkcial. Ekvac. 21, No. 1, pp. 11–41.
[3] Hale, Jack K.; Verduyn Lunel, Sjoerd M. Introduction to functional-differential equations. Applied Mathematical Sciences, 99. Springer-Verlag, New York, (1993).
[4] Hernández, Eduardo; Henríquez, Hernán R. Existence of periodic solutions of partial neutral functional-differential equations with unbounded delay. J. Math. Anal. Appl. 221, No. 2, PP. 499–522, (1998).
[5] Hernández, Eduardo; Henríquez, Hernán R. Existence results for partial neutral functional-differential equations with unbounded delay. J. Math. Anal. Appl. 221 (1998), no. 2, 452–475.
[6] Henríquez, Hernán R. Regularity of solutions of abstract retarded functional-differential equations with unbounded delay. Nonlinear Anal. 28, No. 3, pp. 513–531, (1997).
[7] Henríquez, Hernán R. Periodic solutions of quasi-linear partial functional-differential equations with unbounded delay. Funkcial. Ekvac. 37, No. 2, pp. 329–343, (1994).
[8] Hino, Yoshiyuki; Murakami, Satoru; Yoshizawa, Taro. Existence of almost periodic solutions of some functional differential equations with infinite delay in a Banach space. Tohoku Math. J. (2) 49, No. 1, pp. 133–147, (1997).
[9] Krein, S. G. Linear differential equations in Banach space. Translated from the Russian by J. M. Danskin. Translations of Mathematical Monographs, Vol. 29. American Mathematical Society, Providence, R. I., (1971).
[10] Pazy, A. Semigroups of linear operators and applications to partial differential equations. Applied Mathematical Sciences, 44. Springer-Verlag, New York-Berlin, (1983).
[11] B. N. Sadovskii. On a fixed point principle. Funct. Anal. Appl. 1, pp. 74-76, (1967).
[12] Travis, C. C.; Webb, G. F. Existence and stability for partial functional differential equations. Trans. Amer. Math. Soc. 200, pp. 395–418, (1974).
[2] Hale, Jack K.; Kato, Junji.(1978) Phase space for retarded equations with infinite delay. Funkcial. Ekvac. 21, No. 1, pp. 11–41.
[3] Hale, Jack K.; Verduyn Lunel, Sjoerd M. Introduction to functional-differential equations. Applied Mathematical Sciences, 99. Springer-Verlag, New York, (1993).
[4] Hernández, Eduardo; Henríquez, Hernán R. Existence of periodic solutions of partial neutral functional-differential equations with unbounded delay. J. Math. Anal. Appl. 221, No. 2, PP. 499–522, (1998).
[5] Hernández, Eduardo; Henríquez, Hernán R. Existence results for partial neutral functional-differential equations with unbounded delay. J. Math. Anal. Appl. 221 (1998), no. 2, 452–475.
[6] Henríquez, Hernán R. Regularity of solutions of abstract retarded functional-differential equations with unbounded delay. Nonlinear Anal. 28, No. 3, pp. 513–531, (1997).
[7] Henríquez, Hernán R. Periodic solutions of quasi-linear partial functional-differential equations with unbounded delay. Funkcial. Ekvac. 37, No. 2, pp. 329–343, (1994).
[8] Hino, Yoshiyuki; Murakami, Satoru; Yoshizawa, Taro. Existence of almost periodic solutions of some functional differential equations with infinite delay in a Banach space. Tohoku Math. J. (2) 49, No. 1, pp. 133–147, (1997).
[9] Krein, S. G. Linear differential equations in Banach space. Translated from the Russian by J. M. Danskin. Translations of Mathematical Monographs, Vol. 29. American Mathematical Society, Providence, R. I., (1971).
[10] Pazy, A. Semigroups of linear operators and applications to partial differential equations. Applied Mathematical Sciences, 44. Springer-Verlag, New York-Berlin, (1983).
[11] B. N. Sadovskii. On a fixed point principle. Funct. Anal. Appl. 1, pp. 74-76, (1967).
[12] Travis, C. C.; Webb, G. F. Existence and stability for partial functional differential equations. Trans. Amer. Math. Soc. 200, pp. 395–418, (1974).
Published
2017-05-22
How to Cite
[1]
E. Hernández, “Regularity of solutions of partial neutral functional differential equations with unbounded delay”, Proyecciones (Antofagasta, On line), vol. 21, no. 1, pp. 65-95, May 2017.
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