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To the theory of central dispersions for the linear differential equations \(y''=q(t)y\) of a finite type-special. (English) Zbl 0708.34011

The author presents a certain generalization of the basic concepts involved in Borůvka’s theory of central dispersions for the differential equation \(y''=q(t)y\) on an interval (a,b) with \(-\infty \leq a<b\leq +\infty\). She introduces special central dispersions \(\phi_ n(t)\) and \(\psi_ n(t)\) of first and second kind with arbitrary index n and studies certain algebraic properties of the sets \(G^{(1)}\) and \(G^{(2)}\) which these functions constitute. Introducing still another two kinds of dispersions she obtains finally the set \(\Gamma =G^{(1)}\cup G^{(2)}\cup G^{(3)}\cup G^{(4)}\) of special central dispersions and shows that \(\Gamma\) consists of two finite cyclic groups and two finite sets.
Reviewer: L.Janos

MSC:

34A30 Linear ordinary differential equations and systems
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References:

[1] Borůvka O.: Lineare Differentialtransformationen 2.Ordnung. VEB OVW, Berlin 1967. · Zbl 0153.11201
[2] Laitoch M.: To the theory of linear difference equations. Acta Univ. Palackianae Olomucensis (Olomouc), Fac. Rer. Nat. 79 (1984). · Zbl 0586.39002
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