Effects of varying nonlinearity and their singular perturbation flavour
type: Item
instance of: scholarly article
title: Effects of varying nonlinearity and their singular perturbation flavour
zbMATH Open document ID: 0961.34042
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-09-14T00:00:00Z
review text: The authors consider the second-order differential equation \[ y''+ f(y, p)= 0, \] where \(p\) is a parameter and \(f(\cdot, p)\) is odd, strictly increasing and continuous on \((-\infty, \infty)\). For \(p\to\infty\) the family of functions approaches \(f_0(y)\) which is continuous on \((-a,a)\), the convergence being uniform on \((\varepsilon- a,a-\varepsilon)\). At \(\pm a\) discontinuities are allowed. The convergence of the periodic solutions to those of the ``limit'' equation \[ y''= f_0(y) \] is considered. Further, a study is made for the nonperiodic solutions to \[ y''- f(y, p)= 0. \]
Mathematics Subject Classification ID: 34E10
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1506536
zbMATH Keywords: limit equation
zbMATH Keywords: varying nonlinearity
zbMATH Keywords: convergence of solutions
zbMATH Keywords: nonperiodic solutions
author: U. Elias
author: H. Gingold
reviewed by: Vladimir Răsvan
MaRDI profile type: Publication
OpenAlex ID: W2159375890
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DOI: 10.1006/JMAA.2000.6912
description: scientific article; zbMATH DE number 1506536