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Extremum Condition and Stability Tests for Solutions of Gradient Systems

Extremum Condition and Stability Tests for Solutions of Gradient Systems We study the Lyapunov stability of equilibria of gradient systems. We describe the class of functions generating the right-hand side of a gradient system for which sufficient condition for a nonstrict local minimum are also stability conditions for the equilibria. The corresponding extremum conditions for functions of several variables are given. Stability tests for completely solvable systems with a multidimensional independent variable are stated. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Extremum Condition and Stability Tests for Solutions of Gradient Systems

Differential Equations , Volume 55 (3) – Apr 24, 2019

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References (7)

Publisher
Springer Journals
Copyright
Copyright © 2019 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266119030078
Publisher site
See Article on Publisher Site

Abstract

We study the Lyapunov stability of equilibria of gradient systems. We describe the class of functions generating the right-hand side of a gradient system for which sufficient condition for a nonstrict local minimum are also stability conditions for the equilibria. The corresponding extremum conditions for functions of several variables are given. Stability tests for completely solvable systems with a multidimensional independent variable are stated.

Journal

Differential EquationsSpringer Journals

Published: Apr 24, 2019

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