Integral averages and the asymptotic behavior of solutions of second order ordinary differential equations
type: Item
instance of: scholarly article
title: Integral averages and the asymptotic behavior of solutions of second order ordinary differential equations
zbMATH Open document ID: 0754.34045
DOI: 10.1016/0022-247X(92)90121-S
author: M. Naito
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: Consider the second order differential equation \((*)\;x''+a(t)f(x)=0\), where \(a\in C[t_ 0,\infty)\) and \(f\in C^ 1(\mathbb{R}\backslash\{0\})\). Moreover let \(xf(x)>0\) and \(f'(x)\geq 0\) for \(x\in\mathbb{R}\backslash\{0\}\). Under the hypothesis \(\limsup_{t\to\infty}t^{-1}\int^ t\int^ sa(r)dr ds>-\infty\), that is weaker as the hypothesis used in the previous papers by the author, he proves when \((*)\) has solutions being asymptotically linear.
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 62044
zbMATH Keywords: Emden-Fowler equation
zbMATH Keywords: asymptotically linear solution
zbMATH Keywords: second order differential equation
reviewed by: Dobiesław Bobrowski
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 62044