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Limit behavior of solutions of ordinary linear differential equations. (English) Zbl 0809.34019

The author deals with the set of all linear differential equations \[ y^{(n)}+ p_{n-1}(x) y^{(n-1)}+\cdots+ p_ 0(x) y=0 \] with continuous coefficients on open intervals. The global transformability decomposes the set into classes of equivalent equations.
The goal of the paper is the characterization of each class by means of the \(\omega\)-limit set taken for any \(n\)-tuple of linearly independent solutions.
Reviewer: E.Barvínek (Brno)

MSC:

34A30 Linear ordinary differential equations and systems
34D05 Asymptotic properties of solutions to ordinary differential equations
34A26 Geometric methods in ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
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References:

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