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Annali di Matematica Pura ed Applicata

, Volume 75, Issue 1, pp 385–396 | Cite as

Criterion of periodicity of solutions of a certain differential equation with a periodic coefficient

  • F. Neuman
Article

Summary

In this paper the differential equation (1) y″=q(t)y is considered where q(t) is a real continuous function with period π. There is proved a necessary and sufficient condition for the stability of the trivial solution of Equation (1) when the zeros of the characteristic equation λ2 - Aλ+1=0, coincide. Moreover, there is shown the construction of all Equations (1) admitting only periodic or half-periodic solutions with period π.

Keywords

Differential Equation Continuous Function Characteristic Equation Trivial Solution Periodic Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [1]
    R. Bellman,Stability theory of differential equations, New York, Toronto, London 1953.Google Scholar
  2. [2]
    L. Cesari,Asymptotic behavior and stability problems in ordinary differential equations, Springer Verlag 1959.Google Scholar
  3. [3]
    J. Horn,Gewönliche Differentialgleichungen, Berlin, Leipzig 1937.Google Scholar
  4. [4]
    F. Neuman,Bounded non-periodic solutions of second-order linear differential equations with periodic coefficients, to appear in Canadian Math. J.Google Scholar

Copyright information

© Nicola Zanichelli Editore 1967

Authors and Affiliations

  • F. Neuman
    • 1
  1. 1.BrnoCecoslovacchia

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