# Some Results on Stability of Retarded Functional Differential Equations Using Dichotomic Map Techniques

Some Results on Stability of Retarded Functional Differential Equations Using Dichotomic Map... This paper deals with the study of the stability of nonautonomous retarded functional differential equations using the theory of dichotomic maps. After some preliminaries, we prove the theorems on simple and asymptotic stability. Some examples are given to illustrate the application of the method. Main results about asymptotic stability of the equation \$\$x'(t) = - b(t)x(t - r)\$\$ and of itsnonlinear generalization \$\$x'(t) = b(t)f(x(t - r))\$\$ are established. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Some Results on Stability of Retarded Functional Differential Equations Using Dichotomic Map Techniques

, Volume 2 (3) – Oct 7, 2004
10 pages

/lp/springer_journal/some-results-on-stability-of-retarded-functional-differential-5ywWbPSVKs
Publisher
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1009742807025
Publisher site
See Article on Publisher Site

### Abstract

This paper deals with the study of the stability of nonautonomous retarded functional differential equations using the theory of dichotomic maps. After some preliminaries, we prove the theorems on simple and asymptotic stability. Some examples are given to illustrate the application of the method. Main results about asymptotic stability of the equation \$\$x'(t) = - b(t)x(t - r)\$\$ and of itsnonlinear generalization \$\$x'(t) = b(t)f(x(t - r))\$\$ are established.

### Journal

PositivitySpringer Journals

Published: Oct 7, 2004

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