Positivity of solutions of adapted generalized Riccati equation with consequences in oscillation theory
type: Item
instance of: scholarly article
title: Positivity of solutions of adapted generalized Riccati equation with consequences in oscillation theory
zbMATH Open document ID: 1468.34040
author: Petr Hasil
author: Michal Veselý
published in: Applied Mathematics Letters
publication date: 2021-04-28T00:00:00Z
review text: The authors present a new version of the adapted generalized Riccati equation. A simple condition is given which guarantees that any solution of this equation has to be positive in at least one point. Using this result, the authors establish oscillation criteria for the half-linear differential equation \[ \left( \left( \frac{t}{r(t)} \right)^{p-1}\Phi(x'(t)) \right)'+\frac{s(t)}{t\log^p{t}}\Phi(x(t))=0, \] where \(\Phi(x)=|x|^{p-1}\operatorname{sgn}x\) (\(p>1\)), \(\log\) denotes the natural logarithm, and \(r: [e,\infty)\to (0,\infty)\) and \(s: [e,\infty)\to\mathbb{R}\) are continuous functions such that \[ \int_e^\infty \frac{r(\tau)}{\tau} \, d\tau=\infty, \quad \int_e^\infty \frac{s(\tau)}{\tau\log^p{\tau}} \, d\tau\in\mathbb{R}. \]
reviewed by: Kōdai Fujimoto
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 7340780
zbMATH Keywords: Riccati technique
zbMATH Keywords: Riccati equation
zbMATH Keywords: half-linear equation
zbMATH Keywords: oscillation theory
zbMATH Keywords: oscillation criterion
MaRDI profile type: Publication
full work available at URL: j.aml.2021.107118
OpenAlex ID: W3131662894
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DOI: 10.1016/J.AML.2021.107118
description: scientific article; zbMATH DE number 7340780