Stability of bounded and unbounded sets for ordinary differential equations

  • 70 Accesses

  • 4 Citations


The stability properties of subsets of Rn are examined using a family of Liapunov functions and the invariance properties of the sets.


  1. [1]

    T. A. Burton,An extension of Liapunov's method, J. Math. Anal. Appl.,28 (1969), pp. 545–552.

  2. [2]

    T. A. Burton,Correction to an extension of Liapunov's direct method, J. Math. Anal. Appl.,32 (1970), pp. 689–691.

  3. [3]

    J. R. Haddock,Liapunov functions and boundedness and global existence of solutions, Appl. Anal.,1 (1972), pp. 321–330.

  4. [4]

    J. R. Haddock,Some refinements of asymptotic stability theory, Ann. Mat. Pura Appl., (4),89 (1971), pp. 393–402.

  5. [5]

    J. P. LaSalle,Stability theory for ordinary differential equations, J. Diff. Eqs.,4 (1968), pp. 57–65.

  6. [6]

    Z. Opial,Sur la dependance des solutions d'un systeme d'equations differentielles de leur second membres. Application aux systems presque autonomes, Ann. Polon. Math.,8 (1960), pp. 75–89.

  7. [7]

    A. StraussJ. A. Yorke,On asymptotically autonomous differential equations, Math. Syst. Th.,1 (1967), pp. 175–182.

  8. [8]

    T. Yoshizawa,Asymptotic behavior of solutions of a system of differential equations, Contrib. Differential Eqs.,1 (1963), pp. 371–387.

Download references

Author information

Additional information

Entrata in Redazione l'8 giugno 1972.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Grimmer, R.C., Haddock, J.R. Stability of bounded and unbounded sets for ordinary differential equations. Annali di Matematica 99, 143–153 (1974) doi:10.1007/BF02413722

Download citation


  • Differential Equation
  • Ordinary Differential Equation
  • Stability Property
  • Invariance Property
  • Liapunov Function