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On the structure of the period set of periodic solutions to some linear evolution systems of differential equations

On the structure of the period set of periodic solutions to some linear evolution systems of... ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 6, pp. 797–805.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c Dang Han Hoi, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 6, pp. 780–787. PARTIAL DIFFERENTIAL EQUATIONS On the Structure of the Period Set of Periodic Solutions to Some Linear Evolution Systems of Differential Equations Dang Han Hoi Novgorod State University, Novgorod, Russia Received August 25, 2005 DOI: 10.1134/S0012266107060067 1. It was discovered in [1, 2] that, in the investigation of the problem on periodic solutions of some partial differential equations, the set of periods for which the periodic solution is unique has a rather complicated structure. In the present paper, we study this problem for a special class of linear equations in the space of smooth differential forms on the circle. ∞ k Let C be the space of smooth differential forms on the circle S =Π = R/(2Z), and let H be S S the Sobolev space of differential forms on S whose coefficients have square integrable generalized derivatives of order ≤ k [3]. By A we denote the operator i(d + δ) (the so-called natural differential operator on S), where d is the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

On the structure of the period set of periodic solutions to some linear evolution systems of differential equations

Hoi, Dang
Differential Equations , Volume 43 (6) – Jul 23, 2007
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References (2)

Publisher
Springer Journals
Copyright
Copyright © 2007 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266107060067
Publisher site
See Article on Publisher Site

Abstract

ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 6, pp. 797–805.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c Dang Han Hoi, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 6, pp. 780–787. PARTIAL DIFFERENTIAL EQUATIONS On the Structure of the Period Set of Periodic Solutions to Some Linear Evolution Systems of Differential Equations Dang Han Hoi Novgorod State University, Novgorod, Russia Received August 25, 2005 DOI: 10.1134/S0012266107060067 1. It was discovered in [1, 2] that, in the investigation of the problem on periodic solutions of some partial differential equations, the set of periods for which the periodic solution is unique has a rather complicated structure. In the present paper, we study this problem for a special class of linear equations in the space of smooth differential forms on the circle. ∞ k Let C be the space of smooth differential forms on the circle S =Π = R/(2Z), and let H be S S the Sobolev space of differential forms on S whose coefficients have square integrable generalized derivatives of order ≤ k [3]. By A we denote the operator i(d + δ) (the so-called natural differential operator on S), where d is the

Journal

Differential Equations – Springer Journals

Published: Jul 23, 2007

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