Conjugate points of solutions of an iterated differential equation of the \(n\)-th order. (English) Zbl 0545.34025

Vlček, Vladimír

Acta Univ. Palacki. Olomuc., Fac. Rerum Nat. 76, Math. 22, 115-130 (1983).

The author is concerned with a spacing of null points of oscillatory bands of solutions of an iterated linear differential equation of the n- th order. He introduces the notion of the n-th conjugate point as well as the notion of weakly and strongly conjugate points. He describes the properties of them and uses them for a description of the spacing of null points of an iterated equation.

Reviewer: M.Greguš

MSC:

34C05	Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34A30	Linear ordinary differential equations and systems

Keywords:

spacing of null points; n-th order; conjugate point; iterated equation

References:

[1]	Vlček V.: The first conjugate point of solution of the N-th order iterated differential equation. Acta UP Olom., F. R. N., Tom 73, 1982. · Zbl 0522.34029
[2]	Borůvka O.: Lineare Differentialtransformationen 2. Ordnung. VEB Deutscher Verlag der Wissenschaften, Berlin, 1967. · Zbl 0153.11201
[3]	Sherman T. L.: Properties of solutions of Nth order linear differential equations. Pacific J. Math., Vol. 15, No. 3, 1965. · Zbl 0132.31204 · doi:10.2140/pjm.1965.15.1045
[4]	Vlček V.: Conjugate points of solutions of a fourth-order iterated linear differential equation. Acta UP Olom., F. R. N., Tom 53, 1977.
[5]	Vlček V.: On a distribution of zeros of solutions of a fourth-order iterated linear differential equation. Acta UP Olom., F. R. N., Tom 57, 1978.