Annali di Matematica Pura ed Applicata

, Volume 82, Issue 1, pp 1–15 | Cite as

Non continuous liapunov functions

  • Giorgio P. Szegö
  • Giulio Treccani


Theorems which give sufficient conditions for various kinds of qualitative behaviours of flows defined by ordinary differential equations are proved. These theorems are based upon suitable properties of non continuous real-valued functions and their lower-right-hand-side Dini derivatives along the trajectories of the system.


Differential Equation Ordinary Differential Equation Qualitative Behaviour Suitable Property Liapunov Function 
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  1. [1]
    N. P. Bhatia andG. P. Szegö,Dynamical Systems: Stability Theory and Applications: Lecture Notes in Mathematics, vol. 35, Springer-Verlag, Berlin, Heidelberg, New York, 1967.Google Scholar
  2. [2]
    N. P. Bhatia,Dynamical Systems. InH. W. Kuhn andG. P. Szegö (Editors),Mathematical Systems Theory and Economics, Lecture Notes in Operation Research Springer-Verlag, Berlin, Heidelberg - New York, 1969.Google Scholar
  3. [3]
    J. L. Massera,Contributions to stability theory, Ann. of Math., vol. 64, (1956) pp. 182–206.CrossRefMATHMathSciNetGoogle Scholar
  4. [4]
    J. A. Yorke,Liapunov's Second Method and Non-Lipschitz Liapunov Function, Tech. Note BN-579, Institute for Fluid Dynamics and Applied Mathematics, University of Maryland College Park, Maryland, Oct. 1968.Google Scholar
  5. [5]
    G. P. Szegö andG. Treccani,Sui teoremi del tipo di Rolle in R n, Tech. Rep. IFUM 060/TR Università di Milano, Milano. March 1968.Google Scholar

Copyright information

© Nicola Zanichelli Editore 1969

Authors and Affiliations

  • Giorgio P. Szegö
    • 1
  • Giulio Treccani
    • 1
  1. 1.Milano

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