##
**Ordinary linear differential equations – a survey of the global theory.**
*(English)*
Zbl 0633.34008

Differential equations and their applications, Equadiff 6, Proc. 6th Int. Conf., Brno/Czech. 1985, Lect. Notes Math. 1192, 59-70 (1986).

[For the entire collection see Zbl 0595.00009.]

The paper is an informal survey for second-order linear homogeneous differential equations of the methods of O. Borůvka [Linear differential transformations of the second order (1967; Zbl 0153.112)] as extended by the author to equations of nth-order [e.g., J. Diff. Equations 15, 589-596 (1974; Zbl 0287.34029); Czech. Math. J. 34(109), 645-663 (1984; Zbl 0573.34028)]. The general problem is to characterize the equivalence classes and invariants of such nth-order equations with respect to \(C^ n\)-diffeomorphisms of the dependent and independent variables. The Borůvka technique classifies equations according to the number of zeros of nontrivial solutions. The author and others have successfully applied the techniques to a variety of problems in ordinary differential equations, the geometry of manifolds, differential systems with delays, and functional equations. Details are omitted in this paper, but the author refers to a forthcoming book of his [Ordinary linear differential equations, Prague, Oxford].

The paper is an informal survey for second-order linear homogeneous differential equations of the methods of O. Borůvka [Linear differential transformations of the second order (1967; Zbl 0153.112)] as extended by the author to equations of nth-order [e.g., J. Diff. Equations 15, 589-596 (1974; Zbl 0287.34029); Czech. Math. J. 34(109), 645-663 (1984; Zbl 0573.34028)]. The general problem is to characterize the equivalence classes and invariants of such nth-order equations with respect to \(C^ n\)-diffeomorphisms of the dependent and independent variables. The Borůvka technique classifies equations according to the number of zeros of nontrivial solutions. The author and others have successfully applied the techniques to a variety of problems in ordinary differential equations, the geometry of manifolds, differential systems with delays, and functional equations. Details are omitted in this paper, but the author refers to a forthcoming book of his [Ordinary linear differential equations, Prague, Oxford].

Reviewer: C.Coleman

### MSC:

34A30 | Linear ordinary differential equations and systems |