Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Two-Sided Solutions of Linear Nonautonomous Homogeneous Functional-Differential Equations

Two-Sided Solutions of Linear Nonautonomous Homogeneous Functional-Differential Equations Differential Equations, Vol. 41, No. 10, 2005, pp. 1417–1424. Translated from Differentsial'nye Uravneniya, Vol. 41, No. 10, 2005, pp. 1345–1352. Original Russian Text Copyright c 2005 by Murovtsev. ORDINARY DIFFERENTIAL EQUATIONS Two-Sided Solutions of Linear Nonautonomous Homogeneous Functional-Di erential Equations A. N. Murovtsev Moscow State Textile Academy, Moscow, Russia Received March 29, 2004 1. Two-sided solutions (i.e., solutions de ned on the entire real line R) of linear nonautonomous functional-di erential equations were considered for the rst time in [1] (see [2, 3]) for the case of a small deviation of the argument; the existence and uniqueness theorem for two-sided solutions was proved there in the class of functions bounded at in nity by an exponential. In the case of arbitrary deviations of the argument, the analysis of two-sided solutions of linear nonautonomous equations is much more complicated. An in nite set of linearly independent two-sided solutions was constructed in [4{7] under additional assumptions about the nonautonomous term on the right-hand side in a linear nonautonomous functional-di erential equation. For example, a countable set of linearly independent two-sided solutions of homogeneous delay functional-di erential equation with a nonautonomous term tending to zero as jtj!1 and bounded by an exponential http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Two-Sided Solutions of Linear Nonautonomous Homogeneous Functional-Differential Equations

Murovtsev, A.
Differential Equations , Volume 41 (10) – Dec 12, 2005
Download PDF
8 pages

Loading next page...
 
/lp/springer-journals/two-sided-solutions-of-linear-nonautonomous-homogeneous-functional-z0qUPGWYLn

References (4)

Publisher
Springer Journals
Copyright
Copyright © 2005 by MAIK "Nauka/Interperiodica"
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1007/s10625-005-0293-0
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 41, No. 10, 2005, pp. 1417–1424. Translated from Differentsial'nye Uravneniya, Vol. 41, No. 10, 2005, pp. 1345–1352. Original Russian Text Copyright c 2005 by Murovtsev. ORDINARY DIFFERENTIAL EQUATIONS Two-Sided Solutions of Linear Nonautonomous Homogeneous Functional-Di erential Equations A. N. Murovtsev Moscow State Textile Academy, Moscow, Russia Received March 29, 2004 1. Two-sided solutions (i.e., solutions de ned on the entire real line R) of linear nonautonomous functional-di erential equations were considered for the rst time in [1] (see [2, 3]) for the case of a small deviation of the argument; the existence and uniqueness theorem for two-sided solutions was proved there in the class of functions bounded at in nity by an exponential. In the case of arbitrary deviations of the argument, the analysis of two-sided solutions of linear nonautonomous equations is much more complicated. An in nite set of linearly independent two-sided solutions was constructed in [4{7] under additional assumptions about the nonautonomous term on the right-hand side in a linear nonautonomous functional-di erential equation. For example, a countable set of linearly independent two-sided solutions of homogeneous delay functional-di erential equation with a nonautonomous term tending to zero as jtj!1 and bounded by an exponential

Journal

Differential Equations – Springer Journals

Published: Dec 12, 2005

There are no references for this article.