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Oscillatory behavior of iterative linear ordinary differential equations depends on their order. (English) Zbl 0608.34036

Each iterative ordinary linear homogeneous differential equation of an odd order has nonvanishing solutions regardless of the oscillatory behavior of the iterated second order equation, whereas each solution of any iterative equation of an even order oscillates if the iterated second order equation is oscillatory.

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A30 Linear ordinary differential equations and systems
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
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