Document Details

Document Type : Thesis 
Document Title :
On First-Order Ordinary Differential Equation in Banach Spaces
المعادلات التفاضلية العادية من الرتبة الأولي في فراغات باناخ
 
Subject : Differential equations 
Document Language : English 
Abstract : This thesis is mainly concerned with the question of the uniqueness of solutions of the Cauchy Problem x0 = f(t; x); x(t0) = x0; (1) where f : [t0; t0 + L]  E ! E, L > 0, 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 case [65]. More precisely, Majorana [65] 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 : [t0; t0 + 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 : Ezzat R. Hassan 
Thesis Type : Master Thesis 
Publishing Year : 1434 AH
2013 AD 
Number Of Pages : 62 
Co-Supervisor : Mohammed Sh. Alhuthali 
Added Date : Thursday, September 19, 2013 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
مديحة مبروك الغانميAl-Ghanmi, Madeaha MabroukInvestigatorMaster 

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