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.
Article PDF
Similar content being viewed by others
References
R. Bellman,Stability theory of differential equations, New York, Toronto, London 1953.
L. Cesari,Asymptotic behavior and stability problems in ordinary differential equations, Springer Verlag 1959.
J. Horn,Gewönliche Differentialgleichungen, Berlin, Leipzig 1937.
F. Neuman,Bounded non-periodic solutions of second-order linear differential equations with periodic coefficients, to appear in Canadian Math. J.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Neuman, F. Criterion of periodicity of solutions of a certain differential equation with a periodic coefficient. Annali di Matematica 75, 385–396 (1967). https://doi.org/10.1007/BF02416811
Issue Date:
DOI: https://doi.org/10.1007/BF02416811