Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 157, pp. 1-11.
Title: Existence of solutions in the alpha-norm for partial
differential equations of neutral type with finite delay
Authors: Khalil Ezzinbi (Univ. Cadi Ayyad, Marrakech, Maroc)
Hatem Megdiche (Faculte des Sciences de Gabes, Tunisie)
Amor Rebey (Inst. Superieur des Math., Kairouan, Tunisie)
Abstract:
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.