Nonmonotone equations with large almost periodic forcing terms
type: Item
instance of: scholarly article
title: Nonmonotone equations with large almost periodic forcing terms
zbMATH Open document ID: 1263.34058
author: Juan Campos
author: Massimo Tarallo
published in: Journal of Differential Equations
publication date: 2012-12-20T00:00:00Z
review text: This paper deals with the equation \[ \dot{u}=j(u)+g(u)+ch(t), \] where \(j:\mathbb R\to\mathbb R\) is an increasing homeomorphism of the type \(j(u)=\alpha_+u^+ -\alpha_- u^-\), \(g:\mathbb R \to \mathbb R\) is a bounded function with derivative vanishing at infinity, \(c\) is a parameter and \(h:\mathbb R \to\mathbb R\) is an almost periodic function. The main result gives the existence of a unique almost periodic solution if \(c\) is large enough and \(h\) satisfies a condition related to the size of the set of zeros. More precisely, \[ ||g'||_{\infty} \lambda (H^{-1}(0))<\min \{ \alpha_+ ,\alpha_- \}, \] where \(H:\Omega \to \mathbb R\) is the extension of \(h\) to a compact topological group \(\Omega\) and \(\lambda\) is the corresponding Haar measure.
reviewed by: Rafael Ortega
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 22C05
zbMATH DE Number: 6117521
zbMATH Keywords: almost periodic solutions
zbMATH Keywords: uniqueness
zbMATH Keywords: bounded solutions
zbMATH Keywords: Haar measure
MaRDI profile type: Publication
full work available at URL: j.jde.2012.09.013
OpenAlex ID: W2082371025
DOI: 10.1016/J.JDE.2012.09.013
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description: scientific article; zbMATH DE number 6117521