## On equation y”-q(t)y of finite type, 1-special, with the same central dispersion of the first kind.(English)Zbl 0709.34031

Some properties of linear differential equations of the type $$y''=q(t)y$$ which have the same central dispersion of the first kind on their definition interval are investigated. According to the author central dispersions of the first kind are functions which map “the zeros of an arbitrary solution $$y''$$ of the equation above “onto the zeros of the same solution”.
Reviewer: P.Smith

### MSC:

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

### Keywords:

central dispersion

### 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 [3] Tesaříková E.: To the theory of central dispersions for the linear differential equations y” = q(t)y of a finite type-special. Acta Univ.Palackianae Olomucensis (Olomouc), Fac.Rer.Nat. 88 (1987). · Zbl 0708.34011 [4] Tesaříková E.: On the properties of central dispersions of linear second order differential equations being of finite type-special. Acta Univ.Palackianae Olomucensis (Olomouc), Fac.Rer.Nat. (1989). · Zbl 0713.34012
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