Semi-Hyperbolicity and differential equations with infinite delay
Other Title(s)
شبه الزائدية و المعادلات التفاضلية ذوات التأخير اللانهائي
Dissertant
Thesis advisor
Comitee Members
Musaidah, Basim
Rabi, Iqab Mahmud
al-Taani, Ali Ayid
University
Mutah University
Faculty
Faculty of Science
Department
Department of Mathematics and Statistics
University Country
Jordan
Degree
Master
Degree Date
2004
English Abstract
In this thesis, we review some results regarding the recently proposed, concept of Bi-shadowing in Run and in Banach spaces.
This concept is a stronger version of shadowing as it consists of direct and indirect shadowing.
It was shown in (Al-Naïf et.al., 1995) that semi-hyperbolic Lipchitz mappings in Banach space are Bi-shadowing.
In practice, this is a form of stability of solutions of certain types of differential equations, such as functional differential equations with infinite delay.
Some results, such as, a linear operator is semi-hyperbolic if and only if it is a-contracting and has no spectral values on the unit circle (theorem 2.4.4), and semi- hyperbolic mappings in Banach spaces are (a, / Bi-shadowing with respect to a-contracting comparison mappings (theorem 2.4.6), are established by Al-Naïf et.al (1996).
We apply these results to the linear differential equation with infinite delay x'(t) = Ax(i) + Bx (t-r) on the state space of initial data C° and obtain a Bi-shadowing result for this equation with respect to a non-linear perturbation of the form y'(t) = Ay (t) + By (t~r) + G {yit), yit-r y.
Main Subjects
Topics
No. of Pages
38
Table of Contents
Table of contents.
Abstract.
Chapter one : Statement of the problem.
Chapter two : Review of selected literature.
Chapter three : Delay differential equations.
Chapter four : Main results.
Chapter five : Summary ; conclusions and recommendations.
References.
American Psychological Association (APA)
al-Maayitah, Rabia Karim. (2004). Semi-Hyperbolicity and differential equations with infinite delay. (Master's theses Theses and Dissertations Master). Mutah University, Jordan
https://search.emarefa.net/detail/BIM-304448
Modern Language Association (MLA)
al-Maayitah, Rabia Karim. Semi-Hyperbolicity and differential equations with infinite delay. (Master's theses Theses and Dissertations Master). Mutah University. (2004).
https://search.emarefa.net/detail/BIM-304448
American Medical Association (AMA)
al-Maayitah, Rabia Karim. (2004). Semi-Hyperbolicity and differential equations with infinite delay. (Master's theses Theses and Dissertations Master). Mutah University, Jordan
https://search.emarefa.net/detail/BIM-304448
Language
English
Data Type
Arab Theses
Record ID
BIM-304448
