Extremum Condition and Stability Tests for Solutions of Gradient Systems

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.