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Document Details
Document Type
:
Thesis
Document Title
:
On First-Order Ordinary Differential Equations in Banach Spaces
المعادلات التفاضلية العادية من الرتبة الأولى في فراغات باناخ
Subject
:
mathematics department
Document Language
:
Arabic
Abstract
:
This thesis is mainly concerned with the question of the uniqueness of solutions of the Cauchy Problem x=f(t,x), x(0)=0 (1) where f: [t_0,t_0+L]×E→E , E is a Banach space. A necessary condition for non-uniqueness of solutions for the Cauchy problem, with the aid of an auxiliary scalar equation, is first established. As a consequence new uniqueness criteria are deduced. This result was previously known to hold only in the scalar [64]. More precisely, Majorana [64] found out a very close relation between the number of the roots of a certain auxiliary scalar equation and those of the Cauchy Problem (1), where, f: [t_0,t_0+L]×R→R. Our main approach is to retain this relation in a suitable generalized sense to provide an abstract version of Majorana's result in a finite dimension real (or complex) Banach space. We then generalize this result to infinitely dimensional real Banach spaces. These form our proper participation which are deferred until Chapter 4. The first part of the thesis introduces selected knowledge of basic facts of scalar Cauchy problems, calculus of abstract function, Cauchy problem in abstract spaces and theory of finite as well as infinite dimensional systems of differential equations is required. The presentation of these preliminaries chapters is self-contained and intends to convey a suitable starting point in this thesis.
Supervisor
:
Dr. Ezzat R. Hassan
Thesis Type
:
Master Thesis
Publishing Year
:
1434 AH
2013 AD
Co-Supervisor
:
Dr. Mohammed Sh. Alhuthali
Added Date
:
Tuesday, June 18, 2013
Researchers
Researcher Name (Arabic)
Researcher Name (English)
Researcher Type
Dr Grade
Email
مديحه مبروك الغانمي
Al-Ghanmi, Madeaha Mabrouk
Researcher
Master
Files
File Name
Type
Description
35657.pdf
pdf
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