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On the basin of attraction of dissipative planar vector fields

Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1455)

Abstract

An estimate for the size of the basin of attraction of an equilibrium point for a class of planar dissipative vector fields is given here. Our main result, which generalizes a theorem of Krasowskii, is applied to give several sufficient conditions for global asymptotic stability.

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References

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    Gasull, A., Llibre, J. and Sotomayor, J., Global asymptotic stability of differential equations in the plane, to appear in J. of Diff. Equations, 1990.Google Scholar
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    Hartman, P. and Olech, C., On global asymptotic stability of differential equations, Trans. Amer. Math. Soc. 104 (1962), 159–178.MathSciNetGoogle Scholar
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    Krasowskii, N.N., On the behaviour in the large of the integral curves of a system of two differential equations, Prikl. Mat. Mek. 18 (1954), 149–154. (in russian).Google Scholar
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    Krasowskii, N.N., Stability of Motion, Stanford University Press, Stanford, California 1963.Google Scholar
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    Olech, C., On the global stability of an autonomous system on the plane, Cont. to Diff. Eq. 1 (1963), 389–400.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterra (Barcelona)Spain
  2. 2.Instituto de Matemática Pura e Aplicada Est. Dona Castorina, 110, CEP 22460Rio de Janeiro, R.J.Brazil

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