Change search
ReferencesLink to record
Permanent link

Direct link
Coercive estimates for the solutions of some singular differential equations and their applications
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This Licentiate thesis deals with the study of existence and uniqueness together with coercive estimates for solutions of certain differential equations. The thesis consists of four papers (papers A, B, C and D) and an introduction, which put these papers into a more general frame and which also serves as an overview of this interesting field of mathematics. In the text below the functions r(x), q(x), m(x) etc. are functions on (-∞,+∞), which are different but well defined in each paper. In paper A we study the separation and approximation properties for the differential operator ly=-y″+r(x)y′+q(x)y in the Hilbert space L2 :=L2(R), R=(-∞,+∞), as well as the existence problem for a second order nonlinear differential equation in L2 . Paper B deals with the study of separation and approximation properties for the differential operator ly=-y″+r(x)y′+s(x)‾y′ in the Hilbert spaceL2:=L2(R), R=(-∞,+∞), (here ¯y is the complex conjugate of y). A coercive estimate for the solution of the second order differential equation ly =f is obtained and its applications to spectral problems for the corresponding differential operatorlis demonstrated. Some sufficient conditions for the existence of the solutions of a class of nonlinear second order differential equations on the real axis are obtained. In paper C we study questions of the existence and uniqueness of solutions of the third order differential equation (L+λE)y:=-m(x)(m(x)y′)″+[q(x)+ir(x)+λ]y=f(x), (0.1) and conditions, which provide the following estimate: ||m(x)(m(x)y′)″||pp+||(q(x)+ir(x)+λ)y||pp≤ c||f(x)||pp for a solution y of (0.1). Paper D is devoted to the study of the existence and uniqueness for the solutions of the following more general third order differential equation with unbounded coefficients: -μ1(x)(μ2(x)(μ1(x)y′)′)′+(q(x)+ir(x)+λ)y=f(x). Some new existence and uniqueness results are proved and some normestimates of the solutions are given.

Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2013. , 105 p.
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757
Research subject
URN: urn:nbn:se:ltu:diva-16970Local ID: 0f123f49-ab51-4486-b8e3-53e81e7156c8ISBN: 978-91-7439-560-0OAI: diva2:989962
Godkänd; 2013; 20130208 (rayakh); Tillkännagivande licentiatseminarium 2013-02-26 Nedanstående person kommer att hålla licentiatseminarium för avläggande av teknologie licentiatexamen. Namn: Raya Akhmetkaliyeva Ämne: Matematik/Mathematics Uppsats: Coercive Estimates for the Solutions of some Singular Differential Equations and their Applications Examinator: Professor Lars-Erik Persson, Institutionen för teknikvetenskap och matematik, Luleå tekniska universitet Diskutant: Associate Professor Gabriela Holubová, Department of Mathematics, University of West Bohemia, Czech Republic Tid: Onsdag den 20 mars 2013 kl 10.00 Plats: E246, Luleå tekniska universitetAvailable from: 2016-09-29 Created: 2016-09-29Bibliographically approved

Open Access in DiVA

fulltext(598 kB)0 downloads
File information
File name FULLTEXT01.pdfFile size 598 kBChecksum SHA-512
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Akhmetkaliyeva, Raya
By organisation
Mathematical Science

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

ReferencesLink to record
Permanent link

Direct link