Asymptotic and oscillatory behaviour of solutions of a linear differential equation
type: Item
instance of: scholarly article
title: Asymptotic and oscillatory behaviour of solutions of a linear differential equation
zbMATH Open document ID: 0764.34027
DOI: 10.1016/0377-0427(92)90236-Q
author: Jozef Rovder
published in: Journal of Computational and Applied Mathematics
publication date: 1992-10-26T00:00:00Z
review text: The linear differential equation \((*)\;y^{(n)}+p(t)y^{(k)}+q(t)y=0\) is considered, where \(n,k\) are integers, \(n>1\), \(1\leq k<n\), \(p(t)\), \(q(t)\) are continuous together with some derivatives. The aim of this paper is to derive the oscillatory properties of a fundamental system of solutions of \((*)\) on the base of the asymptotic behaviour of \((*)\) in the author's previous paper [Arch. Math., Brno 22, 193-202 (1986; Zbl 0607.34051)]. The basic suppositions here are \(q''(t)q(t)^{-1-1/2n}\in L[a,\infty)\), \(p(t)q(t)^{-1+(k+1)/n}\in L[a,b)\) for \(n\) even and similar ones for \(n\) odd. \(L[a,\infty)\) denotes the set of Lebesgue integrable complex-valued functions in \([a,\infty)\).
reviewed by: J.Vosmanský
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 69605
zbMATH Keywords: linear differential equation
zbMATH Keywords: oscillatory properties
zbMATH Keywords: asymptotic behaviour
Wikidata QID: Q115363248
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 69605