Electron. J. Diff. Equ., Vol. 2014 (2014), No. 180, pp. 1-16.

Functional differential equations with unbounded delay in extrapolation spaces

Mostafa Adimy, Mohamed Alia, Khalil Ezzinbi

Abstract:
We study the existence, regularity and stability of solutions for nonlinear partial neutral functional differential equations with unbounded delay and a Hille-Yosida operator on a Banach space X. We consider two nonlinear perturbations: the first one is a function taking its values in X and the second one is a function belonging to a space larger than X, an extrapolated space. We use the extrapolation techniques to prove the existence and regularity of solutions and we establish a linearization principle for the stability of the equilibria of our equation.

Submitted May 10, 2013. Published August 25, 2014.
Math Subject Classifications: 35R10, 47D06.
Key Words: Neutral differential equation; infinite delay; extrapolation space; mild solution; semigroup; stability.

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Mostafa Adimy
INRIA Rhône-Alpes, Université Lyon 1
Institut Camille Jordan, 43 Bd. du 11 novembre 1918
F-69200 Villeurbanne Cedex, France
email: mostafa.adimy@inria.fr
Mohamed Alia
Université Cadi Ayyad, Faculté des Sciences Semlalia
Département de Mathématiques
BP. 2390, Marrakesh, Morocco
email: monsieuralia@yahoo.fr
Khalil Ezzinbi
Université Cadi Ayyad, Faculté des Sciences Semlalia
Département de Mathématiques
BP. 2390, Marrakesh, Morocco
email: ezzinbi@ucam.ac.ma

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