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On a class of linear \(n\)-th order differential equations. (English) Zbl 0685.34034
Linear time-varying differential equations of the form \[ y^{(n)}(t)+\sum^{n}_{i=2}p_ i(t)y^{(n-i)}(t)=0,\quad t\in [a,\infty),\quad a\in {\mathbb{R}}, \] with \(p_ i(\cdot)\) real-valued and continuous are considered. Under certain assumptions, existence of solutions without zeros, a comparison theorem, the existence of a bundle of solutions, and properties of nonoscillatory (i.e. the set of zeros is bounded) is presented.
Reviewer: A.Ilchmann

MSC:
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A30 Linear ordinary differential equations and systems
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References:
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