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Extremum Condition and Stability Tests for Solutions of Gradient Systems

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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.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Belarus, Minsk, 220072, Belarus

    L. B. Knyazhishche

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  1. L. B. Knyazhishche
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Correspondence to L. B. Knyazhishche.

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Knyazhishche, L.B. Extremum Condition and Stability Tests for Solutions of Gradient Systems. Diff Equat 55, 340–347 (2019). https://doi.org/10.1134/S0012266119030078

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  • DOI: https://doi.org/10.1134/S0012266119030078

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