Asymptotic formulas for eigenvalues of the indefinite Sturm-Liouville problem with finite number of turn points
type: Item
instance of: scholarly article
title: Asymptotic formulas for eigenvalues of the indefinite Sturm-Liouville problem with finite number of turn points
zbMATH Open document ID: 1026.34030
author: A. V. Dyachenko
published in: Moscow University Mathematics Bulletin
publication date: 2003-04-23T00:00:00Z
review text: The author considers a spectral problem generated by the Sturm-Liouville equation \[ -y''+[\lambda^2f(x)+q(x)]y=0 \] on a finite segment \([A,B]\) with separated boundary conditions. It is assumed that \(f\) and \(g\) are functions smooth enough and \(f(x)\) has a finite number of simple turning points. The main result of the paper is as follows. The eigenvalues of the problem can be set in several series. Each series has an asymptotics with a prescribed number of terms (the number of the asymptotics terms is determined only by the smoothness of \(f\) and \(q\)). For each series the first three terms of asymptotics are determined in the explicit form.
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34L15
Mathematics Subject Classification ID: 34E05
zbMATH DE Number: 1899991
zbMATH Keywords: indefinite Sturm-Liouville problem
zbMATH Keywords: asymptotics
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1899991