Stability by Lyapunov like functions of nonlinear differential equations with non-instantaneous impulses

Ravi Agarwal; D. O’Regan; S. Hristova

doi:10.1007/s12190-015-0961-z

Stability by Lyapunov like functions of nonlinear differential equations with non-instantaneous impulses

Ravi Agarwal
, D. O’Regan
, S. Hristova

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

51 Citations (Scopus)

Abstract

The stability of the solutions of a nonlinear differential equation with noninstantaneous impulses is studied using Lyapunov like functions. In these differential equation we have impulses, which start abruptly at some points and their action continue on given finite intervals. Sufficient conditions for stability, uniform stability and asymptotic uniform stability of the solutions are established. Examples are given to illustrate the results. Also, some of the results are applied to study a dynamical model in Pharmacokinetics.

Original language	English
Pages (from-to)	147-168
Number of pages	22
Journal	Journal of Applied Mathematics and Computing
Volume	53
Issue number	1-2
DOIs	https://doi.org/10.1007/s12190-015-0961-z
Publication status	Published - 1 Feb 2017

Keywords

Lyapunov functions
Non-instantaneous impulses
Stability

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10.1007/s12190-015-0961-z

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abstract = "The stability of the solutions of a nonlinear differential equation with noninstantaneous impulses is studied using Lyapunov like functions. In these differential equation we have impulses, which start abruptly at some points and their action continue on given finite intervals. Sufficient conditions for stability, uniform stability and asymptotic uniform stability of the solutions are established. Examples are given to illustrate the results. Also, some of the results are applied to study a dynamical model in Pharmacokinetics.",

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KW - Non-instantaneous impulses

KW - Stability

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Stability by Lyapunov like functions of nonlinear differential equations with non-instantaneous impulses

Abstract

Keywords

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