Criterion of periodicity of solutions of a certain differential equation with a periodic coefficient
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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.
KeywordsDifferential Equation Continuous Function Characteristic Equation Trivial Solution Periodic Coefficient
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