Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 12
Stable and unstable manifolds for a class of partial functional differential equations with lack of compactness
Abdallah Afoukal, Khalil Ezzinbi, Khalid Hilal
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
October 16, 2021
March 03, 2029
April 15, 2029

Abstract: The suggestion of this work is to investigate the existence of stable and unstable manifolds near hyperbolic equilibrium for some nonlinear partial functional differential equations with finite delay. We start by studying the spectral decomposition of the linearized equation with an assumption more useful than the usual assumption related to the compactness. Next, we use this decomposition with the variation of constants formula given in the literature, to study the stable and unstable manifolds for nonlinear equation as well as we get the estimations of solutions on those manifolds. As a ...