Translator Disclaimer
2019 Stable manifolds for some partial neutral functional differential equations with non-dense domain
Chiraz Jendoubi
J. Integral Equations Applications 31(3): 343-377 (2019). DOI: 10.1216/JIE-2019-31-3-343

Abstract

We investigate the asymptotic solution beha\-vior for the partial neutral functional differential equation$$ \begin{cases} & \frac {d}{dt}\mathcal {D}u_t=(A+B(t))\mathcal {D}u_t+f(t,u_t), \quad \hbox {$t\geq s\geq 0$,} \\ & u_s=\phi \in \mathcal {C}:=C([-r,0],X), \end{cases} $$ where the linear operator $A$ is not necessarily densely defined and satisfies the Hille-Yosida condition, and the delayed part $f$ is assumed to satisfy the $\varphi $-Lipschitz condition, i.e., $\|f(t,\phi )-f(t,\psi )\|\leq \varphi (t)\|\phi -\psi \|_{\mathcal {C}}$. Here $\varphi $ belongs to some admissible spaces and $\phi ,\ \psi \in \mathcal {C}:=C([-r,0],X)$.

More precisely, we prove the existence of stable (respectively, center stable) manifolds when the linear part generates an evolution family having an exponential dichotomy (respectively, trichotomy) on the half positive line. Furthermore, we show that such stable manifold attracts all mild solutions of the considered neutral equation. An example is given to assimilate our theory.

Citation

Download Citation

Chiraz Jendoubi. "Stable manifolds for some partial neutral functional differential equations with non-dense domain." J. Integral Equations Applications 31 (3) 343 - 377, 2019. https://doi.org/10.1216/JIE-2019-31-3-343

Information

Published: 2019
First available in Project Euclid: 2 November 2019

zbMATH: 07159848
MathSciNet: MR4027252
Digital Object Identifier: 10.1216/JIE-2019-31-3-343

Subjects:
Primary: 35R10
Secondary: ‎34D09, 35B40, 37D10, 47D06

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
35 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.31 • No. 3 • 2019
Back to Top