A nonoscillation theorem for Emden--Fowler equations.
type: Item
instance of: scholarly article
title: A nonoscillation theorem for Emden--Fowler equations.
zbMATH Open document ID: 1036.34039
DOI: 10.1016/S0022-247X(02)00357-8
author: James S. W. Wong
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-02-11T00:00:00Z
review text: The author proves a nonoscillation theorem for the second-order Emden-Fowler equation \[ \quad y''+a(x)| y| ^{\gamma-1}y=0, \quad \gamma>0, \tag{E} \] where \(a(x)\) is positive and absolutely continuous on \((0,\infty)\). Let \(\psi(x)=x^{(\gamma+3)/2+\delta}\) where \(\delta\) is any positive number. The following theorem is proved: Let \(\gamma \not =1\). If \(\psi(x)\) satisfies (a) \(\lim_{x\rightarrow \infty} \psi(x)=k>0\) and (b) \(\int^{\infty}| \psi'(x)|\, dx<\infty\), then equation (E) is nonoscillatory.
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 1866657
zbMATH Keywords: Ordinary differential equation
zbMATH Keywords: Nonlinear
zbMATH Keywords: Second order
zbMATH Keywords: Oscillation
zbMATH Keywords: Asymptotic behavior
reviewed by: Zuzana Došlá
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1866657