Levin's comparison theorems for nonlinear second order differential equations
type: Item
instance of: scholarly article
title: Levin's comparison theorems for nonlinear second order differential equations
zbMATH Open document ID: 0867.34020
DOI: 10.1016/0893-9659(96)00090-0
author: Ravi P. Agarwal
author: W. C. Lian
author: Cheh-Chih Yeh
published in: Applied Mathematics Letters
publication date: 1997-08-11T00:00:00Z
review text: This article concerns Levin-type comparison theorems for nonlinear differential equations of type \((1)_i\) \(-(p_ig(y)|y'|^ay')'=q_if_i(y)\), \(i=1,2\), in a closed real interval \(I\), where \(a\) is a constant and \(f_i\), \(g\), \(p_i\), \(q_i\) are functions satisfying: \(f_i\in C(\mathbb{R},\mathbb{R})\cap C^1(\mathbb{R}\setminus\{0\})\), \(g\in C^1(\mathbb{R},\mathbb{R}_+)\), \(p_i\in C^1(I,\mathbb{R}_+)\), \(q_i\in C(I,\mathbb{R})\), and appropriate technical conditions. The theorems contain various sets of sufficient conditions for nontrivial solutions \(u,v\) of \((1)_1\), \((1)_2\), respectively, to satisfy \(|p_1g(u) |u'|^a u'/f_1(u) |> |p_2 g(v)|v' |^a v'/f_2(v) |\) pointwise on \(I\). The proofs employ a generalization of Osgood's inequality. Extensions and examples are included.
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 978088
zbMATH Keywords: Levin-type
zbMATH Keywords: nonlinear differential equations
zbMATH Keywords: generalization
zbMATH Keywords: Osgood's inequality
reviewed by: Charles A. Swanson
MaRDI profile type: Publication
full work available at URL: 0893-9659(96)00090-0
OpenAlex ID: W2065644125
cites work: Q3284806
cites work: Q5584775
cites work: A Levin type comparison theorem and oscillation results for Volterra- Stieltjes integral equations
cites work: A maximum principle for second order nonlinear differential inequalities and its applications
cites work: Q3980009
cites work: Q4750126
cites work: Existence theorems for second order boundary value problems
cites work: A homotopic deformation along \(p\) of a Leray-Schauder degree result and existence for \((| u'| ^{p-2}u')'+f(t,u)=0\), \(u(0)=u(T)=0\), \(p>1\)
cites work: Q4274968
cites work: Lasalle's inequality and uniqueness theorems
cites work: Uniqueness theorems and successive approximations
cites work: Comparison theorems of Levin type
description: scientific article; zbMATH DE number 978088