Electron. J. Diff. Equ., Vol. 2011 (2011), No. 117, pp. 1-12.

S-asymptotically periodic solutions for partial differential equations with finite delay

William Dimbour, Gisele Mophou, Gaston M. N'Guerekata

Abstract:
In this article, we give some sufficient conditions for the existence and uniqueness of S-asymptotically periodic (mild) solutions for some partial functional differential equations. To illustrate our main result, we study a diffusion equation with delay.

Submitted August 11, 2011. Published September 14, 2011.
Math Subject Classifications: 34K05, 34A12, 34A40.
Key Words: S-asymptotically periodic function; mild solution; exponentially stable semigroup; fractional power operator.

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William Dimbour
Laboratoire C.E.R.E.G.M.I.A., Université des Antilles et de La Guyane
Campus Fouillole 97159 Pointe-à-Pitre Guadeloupe (FWI)
email: William.Dimbour@univ-ag.fr
Gisèle M. Mophou
Laboratoire C.E.R.E.G.M.I.A., Université des Antilles et de La Guyane
Campus Fouillole 97159 Pointe-à-Pitre Guadeloupe (FWI)
email: gisele.Mophou@univ-ag.fr
Gaston M. N'Guérekata
Department of Mathematics, Morgan State University
1700 East Cold Spring Lane, Baltimore, MD 21251, USA
email: Gaston.N'Guerekata@morgan.edu, nguerekata@aol.com

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