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Uniform Persistence in Functional Differential Equations

โœ Scribed by H.I. Freedman; S.G. Ruan

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
682 KB
Volume
115
Category
Article
ISSN
0022-0396

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โœฆ Synopsis

In this paper, we investigate the question of uniform persistence for retarded functional differential equations. By utilizing Liapunov-like functions, Razumikhin techniques, and differential inequalities, we are able to establish criteria for uniform persistence analogous to those obtained by others for ordinary differential equations, difference equations, and reaction-diffusion equations. We apply these criteria to some well known biological models with delay. Our results indicate that the conditions which guarantee the existence of an interior equilibrium are enough to ensure uniform persistence. Moreover, these conditions are equivalent to uniform persistence for the cases without delay as well. ยฉ1995 Academic Press, Inc.

๐Ÿ“œ SIMILAR VOLUMES

Uniform Asymptotic Stability of Abstract
Uniform Asymptotic Stability of Abstract Functional Differential Equations
โœ Xinzhi Liu; Dao Yi Xu ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 247 KB

This paper considers a class of abstract functional differential equations. By using Razumikhin technique, we establish several stability criteria, in terms of two measures, which improve some earlier results found in the literature. Several examples are also worked out to demonstrate the advantages