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On a structure of second order linear differential equations with periodic coefficients having the same discriminant. (English) Zbl 0584.34004

Let \(\Delta =\Delta(\lambda)\) be the discriminant of a differential equation \(y''=(q(t)+\lambda)y,\) \(q\in C^ 0({\mathbb{R}})\), \(q(t+\pi)=q(t)\) for \(t\in {\mathbb{R}}\), \(\lambda\in {\mathbb{R}}\). This paper presents all differential equations of the type \(y''=s(t,\lambda)y\), \(s\in C^ 0({\mathbb{R}}\times {\mathbb{R}})\), \(s(t+\pi,\lambda)=s(t,\lambda)\) for \((t,\lambda)\in {\mathbb{R}}\times {\mathbb{R}}\), whose discriminant is equal to \(\Delta(\lambda)\).

MSC:

34A30 Linear ordinary differential equations and systems
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References:

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