Subharmonic solutions of second-order equations arising near harmonic solutions
type: Item
instance of: scholarly article
title: Subharmonic solutions of second-order equations arising near harmonic solutions
zbMATH Open document ID: 0577.34040
DOI: 10.1016/0022-0396(84)90039-1
author: W. S. Loud
published in: Journal of Differential Equations
publication date: 1984-01-01T00:00:00Z
review text: The author completes his study of \(x''+g(x)=Ef(t)\) where g(x) is an infinitely differentiable odd function and f(t) is a \(2\pi\)-periodic even function such that \(f(t+\pi)=-f(t)\) (that is: f is odd harmonic). Suppose for \(E=E_ 0\), solutions of the associated variation equation \(y''+g'[x(t,E)]=0\) are periodic with a period which is a multiple of \(2\pi\). That is, the characteristic multipliers are exp (\(\pm ip| q)\) where p and q are relatively prime integers such that \(0<p<q\). The period of the solutions is 2q\(\pi\). In favorable cases, there are 2q subharmonics if p and q are odd and 4q subharmonics if either is even. Of these exactly half are stable in a sense defined by the author.
Mathematics Subject Classification ID: 34C99
zbMATH DE Number: 3923173
zbMATH Keywords: odd harmonic function
zbMATH Keywords: characteristic multipliers
MaRDI profile type: Publication
full work available at URL: 0022-0396(84)90039-1
OpenAlex ID: W4231970591
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description: scientific article; zbMATH DE number 3923173