The Cauchy problem for the Sturm-Liouville equations and estimates of its solution with respect to the \(\lambda\) parameter
type: Item
instance of: scholarly article
title: The Cauchy problem for the Sturm-Liouville equations and estimates of its solution with respect to the \(\lambda\) parameter
zbMATH Open document ID: 0965.34013
author: V. Ya. Yakubov
published in: Doklady Mathematics
publication date: 2001-01-28T00:00:00Z
review text: Consider the Cauchy problem \[ y''+\lambda\varrho(x) y= 0,\quad x> 0,\quad y(0)= 0,\quad y'(0)= 1,\tag{\(*\)} \] where \(\lambda\) is a numerical parameter and \(\varrho(x)\) is a function summable on \([0,e]\) and satisfying \(0< \varrho_0\leq\varrho(x)\leq \varrho_1\). The author estimates the modulus of a solution \(y(x,\lambda,\varrho)\) to \((*)\) under some additional assumptions on \(\varrho(x)\). Especially, conditions are derived that the estimate \(|y(x,\lambda, \varrho)|\leq c_1/\sqrt\lambda\) holds.
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34L20
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 1557363
zbMATH Keywords: Sturm-Liouville
zbMATH Keywords: estimates
zbMATH Keywords: solution
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1557363