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


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.


Differential Equation Continuous Function Characteristic Equation Trivial Solution Periodic Coefficient 
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    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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