On oscillation of second-order ''sublinear'' differential equations
type: Item
instance of: scholarly article
title: On oscillation of second-order ''sublinear'' differential equations
zbMATH Open document ID: 0542.34029
DOI: 10.1016/0022-247X(84)90078-7
author: N. E. Zubov
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: Consider the differential equation (*) \(x''(t)+t^{\lambda}p(t)f(x)=0\), \(t\in [0,\infty)\). The authors prove that if 0\(\not\equiv p(t)\in C[0,\infty)\) is periodic, with period w, such that \(\int^{w}_{0}p(t)dt\geq 0,\) and f(x) is an odd function such that \(x^{-\alpha}f(x)\) is nondecreasing in \((0,\infty)\) and \(x^{- \beta}f(x)\) is nonincreasing in \((0,\infty)\) for some constants \(\alpha\),\(\beta\) with \(0<\alpha \leq \beta<1\), then the continuable solutions of (*) are oscillatory for \(0<\lambda<1\).
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 3861587
zbMATH Keywords: oscillatory solutions
reviewed by: Tsai-Sheng Liu
MaRDI profile type: Publication
cites work: Q4075816
cites work: On the oscillatory behaviour of a second order nonlinear differential equation
cites work: OSCILLATION THEOREMS FOR A NONLINEAR ANALOGUE OF HILL'S EQUATION
cites work: Integral Averages and the Oscillation of Second Order Ordinary Differential Equations
cites work: On two-functional spaces
cites work: Some oscillation criteria for second-order nonlinear differential equations
cites work: On the Oscillation and Nonoscillation of Second Order Sublinear Equations
description: scientific article; zbMATH DE number 3861587