Electron. J. Diff. Equ., Vol. 2010(2010), No. 157, pp. 1-11.

Existence of solutions in the alpha-norm for partial differential equations of neutral type with finite delay

Khalil Ezzinbi, Hatem Megdiche, Amor Rebey

In this work, we prove results on the local existence of mild solution and global continuation in the alpha-norm for some class of partial neutral differential equations. We suppose that the linear part generates a compact analytic semigroup. The nonlinear part is just assumed to be continuous. We use the compactness method, to show the main result of this work.

Submitted June 28, 2010. Published October 29, 2010.
Math Subject Classifications: 34K30, 47D06.
Key Words: Neutral equation; analytic semigroup; fractional power; phase space; mild solution; Sadovskii's fixed point theorem.

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Khalil Ezzinbi
Université Cadi Ayyad, Faculté des Sciences Semlalia
Département de Mathématiques, BP 2390, Marrakech, Maroc
email: ezzinbi@gmail.com
Hatem Megdiche
Département de Mathématiques, Faculté des Sciences de Gabès
Cité Erriadh 6072, Zrig, Gabès, Tunisie
email: megdichehatem@yahoo.fr
Amor Rebey
Institut Supérieur des Mathématiques Appliquées et de l'Informatique de Kairouan
Avenue Assad Iben Fourat - 3100 Kairouan, Tunisie
email: rebey_amor@yahoo.fr

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