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


34A30 Linear ordinary differential equations and systems
Full Text: EuDML


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.