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Functional differential equations with unbounded delay in extrapolation spaces

Mostafa Adimy 1, 2, 3, * Mohamed Alia 4 Khalil Ezzinbi 4
* Corresponding author
1 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire, Inria Grenoble - Rhône-Alpes, ICJ - Institut Camille Jordan [Villeurbanne]
3 MMCS - Modélisation mathématique, calcul scientifique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : We study the existence, regularity and stability of solutions for nonlinear partial neutral functional differential equations with unbounded de-lay and a Hille-Yosida operator on a Banach space X. We consider two non-linear 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 regu-larity of solutions and we establish a linearization principle for the stability of the equilibria of our equation.
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Mostafa Adimy, Mohamed Alia, Khalil Ezzinbi. Functional differential equations with unbounded delay in extrapolation spaces. Electronic Journal of Differential Equations, Texas State University, Department of Mathematics, 2014, 2014, pp.1 - 16. ⟨hal-01096950⟩

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