Periodic solutions of the Hill equation
type: Item
instance of: scholarly article
title: Periodic solutions of the Hill equation
zbMATH Open document ID: 1315.34064
published in: Journal of Mathematical Sciences (New York)
publication date: 2014-10-10T00:00:00Z
review text: The author studies the Hill equation \[ y''(t)+Ty(t)=0 \] in a Hilbert space \(H\) with periodic conditions \(y(0)=y(w); y'(0)=y'(w).\) By transforming the above equation into a first order differential equation in the space \(H_T=D(T^{1/2})\bigoplus D(T^{1/2})\) and using the semi-group formula, he shows that it is solvable and that the solutions can be expressed in terms of the generalized Green's operator.
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34B27
zbMATH DE Number: 6353852
zbMATH Keywords: Hill equation
zbMATH Keywords: periodic solution
author: O. O. Pokutnyj
MaRDI profile type: Publication
full work available at URL: s10958-014-1707-4
OpenAlex ID: W1987299066
cites work: Q5587978
cites work: Q5662630
cites work: Periodic problems of difference equations and ergodic theory
cites work: Q5531981
cites work: Q4674795
DOI: 10.1007/S10958-014-1707-4
description: scientific article; zbMATH DE number 6353852