On the convergence of sequences of ordinary differential equations
type: Item
instance of: scholarly article
title: On the convergence of sequences of ordinary differential equations
zbMATH Open document ID: 1076.47033
author: Yanyan Li
published in: Mathematical Notes
publication date: 2004-12-07T00:00:00Z
review text: The complex differential expression \[ l(y)=\sum_{k=0}^\infty(-1)^{n-k}(p_ky^{(n-k)})^{n-k}, \quad 0\leq x\leq 1, \] with bounday condition \[ By^\wedge+Cy^\vee=0 \] is considered in this paper, where \(p_k\in C^{n-k}[0,1]\) with \(\operatorname {Re} p_0(x)>\varepsilon>0\) for all \(x\in [0,1], \) \(B\) and \(C\) are in \(M_{2n}(\mathbb C),\) \(y^\wedge \) and \(y^\vee \) are some kind of boundary data of \(y.\) The author shows that a singular differential expression of type (1) with condition (2) can be regarded as a limit of a regular differential expression of type (1) with condition (2) if the requirement \[ B^{-1}\operatorname {im}C= \mathbb C^{2n} \circleddash \operatorname {ker}C \] on the boundary condition is satisfied, where \(B^{-1}\) denotes the preimage of \(B.\)
reviewed by: Chung-Tsun Shieh
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 2121433
zbMATH Keywords: regular differential expression
zbMATH Keywords: singular differential expression
zbMATH Keywords: boundary condition
zbMATH Keywords: ordinary differential operator
zbMATH Keywords: sequences of ordinary differential operators
zbMATH Keywords: Sturm-Liouville operator
zbMATH Keywords: singular potential
zbMATH Keywords: singular boundary value problem
MaRDI profile type: Publication
full work available at URL: b:matn.0000030996.52085.e3
OpenAlex ID: W2058513936
DOI: 10.1023/B:MATN.0000030996.52085.E3
description: scientific article; zbMATH DE number 2121433