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Monatshefte für Mathematik

, Volume 166, Issue 1, pp 57–72 | Cite as

Every ordinary differential equation with a strict Lyapunov function is a gradient system

  • Tomáš Bárta
  • Ralph Chill
  • Eva Fašangová
Article

Abstract

We explain and prove the statement from the title. This allows us to formulate a new type of gradient inequality and to obtain a new stabilization result for gradient-like ordinary differential equations.

Keywords

Strict Lyapunov function Gradient system Kurdyka–Łojasiewicz gradient inequality Convergence to equilibrium Damped second order ordinary differential equation 

Mathematics Subject Classification (2000)

37B25 34D05 34C40 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Mathematical AnalysisCharles UniversityPraha 8Czech Republic
  2. 2.Laboratoire de Mathématiques et Applications de Metz et CNRSUniversité Paul Verlaine, Metz, UMR 7122Metz Cedex 1France
  3. 3.Institut für Angewandte AnalysisUniversität UlmUlmGermany

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