The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.
References
[1]
Arend, W. and Bu, S. (2002) The Operator-Valued Marcinkiewicz Multiplier Theorem and Maximal Regularity. Mathematische Zeitschrift, 240, 311-343. http://dx.doi.org/10.1007/s002090100384
[2]
Lizama, C. (2006) Fourier Multipliers and Perodic Solutions of Delay Equatons in Banach Spaces. Journal of Mathematical Analysis and Applications, 324, 921-933. http://dx.doi.org/10.1016/j.jmaa.2005.12.043
[3]
Henriquez, H.R., Pierri, M. and Prokopczyk, A. (2012) Periodic Solutions of Abstract Neutral Functional Differential Equations. Journal of Mathematical Analysis and Applications, 385, 608-621. http://dx.doi.org/10.1016/j.jmaa.2011.06.078
[4]
Benkhalti, R., Bouzahir, H. and Ezzinbi, K. (2001) Existence of a Periodic Solution for Some Partial Functional Differential Equations with Infinite Delay. Journal of Mathematical Analysis and Applications, 256, 257-280. http://dx.doi.org/10.1006/jmaa.2000.7321
[5]
Adimy, M., Bouzahir, H. and Ezzinbi, K. (2004) Existence and Stability for Some Partial Nentral Functional Differential Equations with Infinite Delay. Journal of Mathematical Analysis and Applications, 294, 438-461. http://dx.doi.org/10.1016/j.jmaa.2004.02.033
[6]
Adimy, M., Ezzinbi, K. and Laklach, M. (2000) Local Existence and Global Continuation for a Class of Partial Neutral Functional Differential Equations. Comptes Rendus de l’Académie des Sciences—Series I—Mathematics, 330, 957-962.
[7]
Adimy, M. and Ezzinbi, K. (1998) A Class of Linear Partial Neutral Functional Differential Equations with Non-Dense Domain. Journal of Differential Equations, 147, 285-332. http://dx.doi.org/10.1006/jdeq.1998.3446
[8]
Adimy, M and Ezzinbi, K. (1998) Local Existence and Linearized Stability for Partial Functional Differential Equations. Dynamic Systems and Applications, 7, 389-404.
[9]
Bourgain, J. (1983) Some Remarks on Banach Spaces in Which Martingale Differences Sequences Are Unconditional. Arkiv för Matematik, 21, 163-168. http://dx.doi.org/10.1007/BF02384306
