Weighted boundary value problems for a second-order ordinary differential equation with singularity. I
type: Item
instance of: scholarly article
title: Weighted boundary value problems for a second-order ordinary differential equation with singularity. I
zbMATH Open document ID: 0648.34017
DOI: 10.1007/BF00971919
author: S. H. Smith
published in: Lithuanian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: The author considers the differential equation \(y''+p(x)y'-q(x)=f(x)\) on some interval (0,a], \(a>0\) with complex valued coefficients p, q and f, continuous in (0,a] and having, in general a singularity at \(x=0^+\), and studies the following boundary value problems for this equation: \(\lim_{x\to 0^+}\nu (x)y(x)=C_ 0\) \(y(a)=C_ 0\) and \(\lim \tau (x)y'(x)=C_ 0,\) \(y(a)=C_ a\), where \(C_ 0\), \(a_ 0\) are given complex numbers and where the weight functions \(\nu\) and \(\tau\) naturally depend on the singularities of p and q. The main result concerns the asymptotic properties of solutions to these problems in the case f(x)\(\equiv 0\).
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 4057948
zbMATH Keywords: complex valued coefficients
zbMATH Keywords: weight functions
Wikidata QID: Q115394658
reviewed by: Ludvík Janoš
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4057948