## Differential and Integral Equations

### Stable and unstable manifolds for nonlinear partial neutral functional differential equations

#### Abstract

The aim of this work is to investigate the asymptotic behavior of solutions near hyperbolic equilibria for nonlinear partial neutral functional differential equations. We suppose that the linear part $A$ satisfies the Hille-Yosida condition on a Banach space and is not necessarily densely defined; the delayed part is assumed to be Lipschitz. We show the existence of stable and unstable manifolds near hyperbolic equilibria when the neutral operator is stable and the semigroup generated by the part of $A$ in $\overline{D(A)}$ is compact. Local stable and unstable manifolds are also obtained when the undelayed part is a C$^{1}$ function in a neighborhood of the equilibria.

#### Article information

Source
Differential Integral Equations, Volume 23, Number 7/8 (2010), 773-794.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019195

Mathematical Reviews number (MathSciNet)
MR2654269

Zentralblatt MATH identifier
1240.34337

#### Citation

Benkhalti, Rachid; Ezzinbi, Khalil; Fatajou, Samir. Stable and unstable manifolds for nonlinear partial neutral functional differential equations. Differential Integral Equations 23 (2010), no. 7/8, 773--794. https://projecteuclid.org/euclid.die/1356019195