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

Learn More →

The Samoilenko Reduction Principle for Differential Equations with Random Perturbations

The Samoilenko Reduction Principle for Differential Equations with Random Perturbations Di erential Equations, Vol. 37, No. 2, 2001, pp. 234{239. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 2, 2001, pp. 218{222. Original Russian Text Copyright c 2001 by Stanzhitskii. ORDINARY DIFFERENTIAL EQUATIONS The Samoilenko Reduction Principle for Di erential Equations with Random Perturbations A. N. Stanzhitskii Kiev University, Kiev, Ukraine Received March 23, 1999 The stability problem for an invariant set that is stable if the initial data belong to some manifold containing this set is well known in di erential equations. This problem was solved in [1] for the case in which the invariant set degenerates into a singleton. (This result is well known as the reduction principle in stability theory.) Samoilenko [2, Chap. 2, Sec. 3] proved a similar result for the general case. The aim of the present research is to generalize this result to equations with random perturba- tions of the form dx=dt = F (x)+ (t;x)(t); (1) where t  0, x 2 R ,and (t) is a random process de ned on some probability space ( ; F ; P)and absolutely integrable with probability 1 on every nite interval of the half-line t  0. We suppose that F and  are http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

The Samoilenko Reduction Principle for Differential Equations with Random Perturbations

Stanzhitskii, A.
Differential Equations , Volume 37 (2) – Oct 17, 2004
Download PDF
6 pages

Loading next page...
 
/lp/springer-journals/the-samoilenko-reduction-principle-for-differential-equations-with-KH0tQkee8b

References (0)

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
Springer Journals
Copyright
Copyright © 2001 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/A:1019213709112
Publisher site
See Article on Publisher Site

Abstract

Di erential Equations, Vol. 37, No. 2, 2001, pp. 234{239. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 2, 2001, pp. 218{222. Original Russian Text Copyright c 2001 by Stanzhitskii. ORDINARY DIFFERENTIAL EQUATIONS The Samoilenko Reduction Principle for Di erential Equations with Random Perturbations A. N. Stanzhitskii Kiev University, Kiev, Ukraine Received March 23, 1999 The stability problem for an invariant set that is stable if the initial data belong to some manifold containing this set is well known in di erential equations. This problem was solved in [1] for the case in which the invariant set degenerates into a singleton. (This result is well known as the reduction principle in stability theory.) Samoilenko [2, Chap. 2, Sec. 3] proved a similar result for the general case. The aim of the present research is to generalize this result to equations with random perturba- tions of the form dx=dt = F (x)+ (t;x)(t); (1) where t  0, x 2 R ,and (t) is a random process de ned on some probability space ( ; F ; P)and absolutely integrable with probability 1 on every nite interval of the half-line t  0. We suppose that F and  are

Journal

Differential Equations – Springer Journals

Published: Oct 17, 2004

There are no references for this article.