Periodic solutions of Duffing equation with an asymmetric nonlinearity and a deviating argument
type: Item
instance of: scholarly article
title: Periodic solutions of Duffing equation with an asymmetric nonlinearity and a deviating argument
zbMATH Open document ID: 1302.34104
DOI: 10.1155/2013/507854
author: Zaihong Wang
author: Jin Li
author: Tiantian Ma
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: The paper considers a time delay variant of a Duffing type equation introduced by Fučik, namely, \[ x''+ax^+ - bx^- +g(x(t-\tau) = p(t) \] with \(a, b\) constants subject to \(1/\sqrt{a}+1/\sqrt{b}=2/n\), \(n \in N\), \(\tau \in [0, 2 \pi]\) and \(p: \mathbb R \rightarrow \mathbb R\) is continuous and \(2 \pi\)-periodic. The following result is proved. Consider the above equation under the aforementioned basic assumptions. Assume that \(\lim_{x \rightarrow \pm \infty} g(x)\) exists and is finite. Under specific additional assumptions on equation's coefficients and data, existence of at least one \(2 \pi\)-periodic solution is enshured.
Mathematics Subject Classification ID: 34K13
zbMATH DE Number: 6306954
zbMATH Keywords: periodic solutions
zbMATH Keywords: deviating argument
Wikidata QID: Q58916944
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/507854
OpenAlex ID: W2001430726
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description: scientific article; zbMATH DE number 6306954