Exact multiplicity and stability of periodic solutions for a Duffing equation
type: Item
instance of: scholarly article
title: Exact multiplicity and stability of periodic solutions for a Duffing equation
zbMATH Open document ID: 1267.34069
author: Yanyan Li
published in: Mediterranean Journal of Mathematics
publication date: 2013-03-20T00:00:00Z
review text: The aim of this paper is to prove new results on the exact multiplicity and stability of \(2\pi\)-periodic solutions of the damped Duffing equation \[ x''+cx'+g(t,x)=h(t). \] The proof is based on a known connection between stability and topological index (see, for instance, [\textit{R. Ortega}, NATO ASI Ser., Ser. C, Math. Phys. Sci. 472, 377--409 (1995; Zbl 0834.34058)]), together with some delicate \(L^p\) estimates for periodic and antiperiodic eigenvalues by \textit{M. Zhang} and \textit{W. Li} [Proc. Am. Math. Soc. 130, No. 11, 3325--3333 (2002; Zbl 1007.34053)].
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6147181
zbMATH Keywords: Hill's equation
zbMATH Keywords: periodic solution
zbMATH Keywords: resonance
zbMATH Keywords: stability index
zbMATH Keywords: topological degree
MaRDI profile type: Publication
full work available at URL: s00009-012-0189-1
OpenAlex ID: W2104192849
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DOI: 10.1007/S00009-012-0189-1
description: scientific article; zbMATH DE number 6147181