M.Sc Tezi Görüntüleme

Student:	Neslihan BAYRAM
Supervisor:	Asst.Prof.Dr. Haskız COSKUN
Department:	Mathematics
Institution:	Graduate School of Natural and Applied Sciences
University:	Karadeniz Technical University, Turkey

Title of the Thesis:	Asymptotics of Eigenvalues for Regular Sturm-Liouville Problems
Level:	M.Sc
Acceptance Date:	26/1/2005
Number of Pages:	82
Registration Number:	i1549

Summary:

In this thesis we obtain asymptotic estimates for the eigenvalues of

(a_1)y(a)-(a_2)y'(a)= Lamda((a_1)'y(a)-(a_2)'y'(a)), (a_1),(a_2),(a_1)',(a_2)'-ler reel

reel regular Sturm-Liouville problem having the eigenparameter in the boundary condition when is smooth enough.

In the first part of the study we introduce Sturm-Liouville problems and related theory. We state some important results including asymptotic estimates for solutions without proof. We also give series reversion method which is used to obtain estimates in the following chapter.

In the second part; we use Riccati transformation to create a first-order non-linear equation which is used to approximate to a solution of (7). The conditions under which the boundary conditions (8)-(9) satisfied are determined. We finally, perfom a reversion of the resulting expansion to obtain asymptotic estimates for the eigenvalues.

Keywords: Sturm-Liouville problems, Eigenvalues, Eigenparameter, Asymptotics.