Existence of periodic solutions of neutral functional differential equations with unbounded delay
DOI:
https://doi.org/10.4067/S0716-09172000000300006Keywords:
Abstract retarded functional, semigroups of linear operators, funcional abstracta con retardo, semigrupos de operadores lineales.Abstract
In this work we establish a result of existence of periodic solutions for quasi-linear partial neutral functional differential equations with unbounded delay on a phase space defined axiomatically.References
[1] K. Deimling, Non Linear Functional Analysis, Springer-Verlag, Berlin, (1985).
[2] N. Dunford and J. T. Schwartz, Linear Operators. Part I, John Wiley and Sons, New York, (1988).
[3] J. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcialaj Ekvac., 21, pp. 11-41, (1978).
[4] H. R. Henríquez, Periodic solutions of quasi-linear partial functional differential equations with unbounded delay. Funkcialaj Ekvac. 37 (2), pp. 329-343, (1994).
[5] H. R. Henríquez, On non-exact controllable systems, Int. J. Control, 42(1), pp. 71-83, (1985).
[6] E. Hernández and H. R. Henríquez, Existence Results for partial neutral functional differential equations with unbounded delay, J. Math. Anal. Appl. 221, pp. 452-475, (1998).
[7] E. Hernández and H. R. Henríquez, Existence of periodic solutions of partial neutral functional differential equations with unbounded delay. J. Math. Anal. Appl., 221, pp. 499-522, (1998).
[8] Y. Hino, S. Murakami and T. Naito, Functional Differential Equations with Infinite Delay, Lect. Notes in Maths., 1473. SpringerVerlag, Berlin, (1991).
[9] C-M. Marle, Mesures et Probabilit´es, Hermann, Paris, (1974).
[10] R. H. Martin, Nonlinear Operators & Differential Equations in Banach Spaces, Robert E. Krieger Publ. Co., Florida, (1987).
[11] R. Nagel, One-parameter Semigroups of Positive Operators, Lect. Notes in Maths. 1184 (editor), Springer-Verlag, Berlin, (1986).
[12] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, (1983).
[13] B. N. Sadovskii, On a fixed point principle. Funct. Anal. Appl., 1, pp. 74-76, (1967).
[14] S. J. Shin, An existence theorem of a functional differential equation, Funkcialaj Ekvac. 30, pp. 19-29, (1987).
[2] N. Dunford and J. T. Schwartz, Linear Operators. Part I, John Wiley and Sons, New York, (1988).
[3] J. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcialaj Ekvac., 21, pp. 11-41, (1978).
[4] H. R. Henríquez, Periodic solutions of quasi-linear partial functional differential equations with unbounded delay. Funkcialaj Ekvac. 37 (2), pp. 329-343, (1994).
[5] H. R. Henríquez, On non-exact controllable systems, Int. J. Control, 42(1), pp. 71-83, (1985).
[6] E. Hernández and H. R. Henríquez, Existence Results for partial neutral functional differential equations with unbounded delay, J. Math. Anal. Appl. 221, pp. 452-475, (1998).
[7] E. Hernández and H. R. Henríquez, Existence of periodic solutions of partial neutral functional differential equations with unbounded delay. J. Math. Anal. Appl., 221, pp. 499-522, (1998).
[8] Y. Hino, S. Murakami and T. Naito, Functional Differential Equations with Infinite Delay, Lect. Notes in Maths., 1473. SpringerVerlag, Berlin, (1991).
[9] C-M. Marle, Mesures et Probabilit´es, Hermann, Paris, (1974).
[10] R. H. Martin, Nonlinear Operators & Differential Equations in Banach Spaces, Robert E. Krieger Publ. Co., Florida, (1987).
[11] R. Nagel, One-parameter Semigroups of Positive Operators, Lect. Notes in Maths. 1184 (editor), Springer-Verlag, Berlin, (1986).
[12] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, (1983).
[13] B. N. Sadovskii, On a fixed point principle. Funct. Anal. Appl., 1, pp. 74-76, (1967).
[14] S. J. Shin, An existence theorem of a functional differential equation, Funkcialaj Ekvac. 30, pp. 19-29, (1987).
Published
2017-06-14
How to Cite
[1]
H. R. Henríquez Miranda, “Existence of periodic solutions of neutral functional differential equations with unbounded delay”, Proyecciones (Antofagasta, On line), vol. 19, no. 3, pp. 305-329, Jun. 2017.
Issue
Section
Artículos
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
