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Stability of a scaler differential equation


Author: R. Grimmer
Journal: Proc. Amer. Math. Soc. 32 (1972), 452-456
MSC: Primary 34.51
DOI: https://doi.org/10.1090/S0002-9939-1972-0288369-5
MathSciNet review: 0288369
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Abstract: Sufficient conditions are given for the stability and asymptotic stability of the zero solution of a scalar differential equation frequently encountered in the comparison method.


References [Enhancements On Off] (What's this?)

  • [1] F. Brauer, Some refinements of Lyapunov's second method, Canad. J. Math. 17 (1965), 811-819. MR 31 #3670. MR 0179422 (31:3670)
  • [2] T. G. Hallam and J. W. Heidel, Structure of the solution set of some first order differential equations of comparison type, Trans. Amer. Math. Soc. 160 (1971), 501-512. MR 0281995 (43:7709)
  • [3] V. Lakshmikantham and S. Leela, Differential and integral inequalities: Theory and applications. Vol. 1 : Ordinary differential equations, Math. in Science and Engineering, vol. 55, Academic Press, New York, 1969.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0288369-5
Keywords: Stability, asymptotic stability, nonuniqueness
Article copyright: © Copyright 1972 American Mathematical Society

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