Asymptotic formulae of Liouville--Green type for higher even-order equations
type: Item
instance of: scholarly article
title: Asymptotic formulae of Liouville--Green type for higher even-order equations
zbMATH Open document ID: 1085.34042
author: A. S. A. Al-Hammadi
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2005-05-12T00:00:00Z
review text: The asymptotic formulae of Liouville-Green type of the fundamental solutions of the \(2m\)th-order differential equation \[ (p_0y^{(m)})^{(m)}+\sum\limits_{j=0}^{m-1}\Big[\dfrac12\big\{(q_{m-j}y^{(j)})^{(j+1)}+ (q_{m-j}y^{(j+1)})^{(j)}\big\}+(p_{m-j}y^{(j)})^{(j)}\Big]=0 \eqno(1) \] are investigated. A theorem on the asymptotic behaviour at infinity of the fundamental solutions of (1) is proved. The author shows that some results known earlier are contained in this theorem as particular cases.
reviewed by: Sergei A. Mazanik
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 2167747
zbMATH Keywords: even-order differential equation
zbMATH Keywords: Liouville-Green formulae
zbMATH Keywords: asymptotic form of solution
MaRDI profile type: Publication
full work available at URL: j.cnsns.2004.02.001
OpenAlex ID: W2093608360
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DOI: 10.1016/J.CNSNS.2004.02.001
description: scientific article; zbMATH DE number 2167747