A note on disfocality
type: Item
instance of: scholarly article
title: A note on disfocality
zbMATH Open document ID: 0651.34031
DOI: 10.1016/0022-247X(88)90193-X
author: S. Markvorsen
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: Consider the initial value problem \[ (*):\quad (g(s)p'(s))'+f(s)p(s)=0,\quad p(0)=1,\quad p'(0)=0,\quad s\in [0,\infty[, \] where f and g are given continuous functions and \(g(s)>0\) for all s. If the solution p has a zero, then it has a smallest zero, which is denoted by \(\xi(*)\). The following assertions are proved: Let f(s)g(s)\(\leq k\) 2 for some \(k\in {\mathbb{R}}\) and all \(s\in [0,c]\). 1. If Q(s)\(\leq \pi /4\) for all \(s\in [0,c]\), where Q is defined in terms of f,g and k, then the initial value problem (*) has \(\xi(*)>c\). 2. If \(\int^{c}_{0}k^{-1}f(t)dt\geq \pi/2,\) then \(\xi(*)\leq c\).
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34A12
zbMATH DE Number: 4061686
zbMATH Keywords: Sturm comparison theorems
zbMATH Keywords: Prüfer transformation
Wikidata QID: Q61978228
reviewed by: A. Klíč
MaRDI profile type: Publication
cites work: Disconjugacy of Second-Order Linear Differential Equations with Non-Negative Coefficients
cites work: Consecutive Zeros of Solutions of Ordinary Second Order Differential Equations
cites work: Q5330830
cites work: On an Oscillation Criterion of Liapounoff
cites work: On Lyapunov's inequality for disfocality
cites work: Q4078376
full work available at URL: 0022-247x(88)90193-x
OpenAlex ID: W2051579542
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description: scientific article; zbMATH DE number 4061686