On oscillating differential equations of third order
type: Item
instance of: scholarly article
title: On oscillating differential equations of third order
zbMATH Open document ID: 0964.34027
published in: Moscow University Mathematics Bulletin
publication date: 2001-02-07T00:00:00Z
review text: The equation \[ y^{(n)} = p(t)y \] with \( p(t) \in L_{\text{loc}}(\mathbb{R}_+) \) possesses the property A, if every nontrivial solution to this equation is oscillating for even \(n\) and is either oscillating or satisfies \[ y(t)y'(t)<0\quad\text{for}\quad t\geq t_0, \] for odd \(n\). The author sets out the following assertion. Let \(p(t) \in L_{\text{loc}}(\mathbb{R}_+)\), \(p(t)\leq 0\) for \(t\in \mathbb{R}_+ \) and \[ \int_1^{+\infty} t^2\biggl(p(t) + \frac{2\sqrt{3}}{9} t^{-3}\biggr) dt = -\infty. \] Then the equation \(y''' = p(t)y\) possesses the property~\(A\).
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 1562173
zbMATH Keywords: third-order equation
zbMATH Keywords: oscillating solutions
author: Moubariz Z. Garaev
reviewed by: A. A. Martynyuk
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1562173