Abstract
It is shown that the differential equation
wheren≥2 andp: [a, b] →R is a summable function, is not conjugate in the segment [a, b], if for somel∈{1,...,n−1}, α∈]a,b[, and β∈]α,b[ the inequalities
, hold.
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References
I.T. Kiguradze, Some singular boundary value problems for ordinary differential equations. (Russian)Tbilisi University Press, Tbilisi, 1975.
V.A. Kondratyev, On oscillations of solutions of the equationy (n) =p(x)y. (Russian)Trudy Moskov. Mat. Obshch. 10(1961), 419–436.
N.L. Korshikova, On zeroes of solutions of linear equations of high orders. (Russian)Differential Equations and Their Applications (Russian), 143–148,Moscow University Press Moscow, 1984.
A.Yu. Levin, Non-oscillation of solutions of the equationx (n) +p 1 (t)x (n−1)+ ... +p n (t)x=0. (Russian)Uspekhi Mat. Nauk. 24(1969), No. 2, 43–96.
A.G. Lomtatidze, On oscillatory properties of solutions of linear differential equations of second order. (Russian)Reports of the seminar of the I.N. Vekua Institute of Applied Mathematics,19(1989), 39–54.
T.A. Chanturia, Sturm type theorems of comparison for differential equations of high orders. (Russian)Bull. Acad. Sci. Georgian SSR 99(1980), No. 2, 289–291.
—, On oscillations of solutions of linear differential equations of high orders. (Russian)Reports of the seminar of the I.N. Vekua Institute of Applied Mathematics,16(1982), 3–72.
F. Hartman, Ordinary differential equations. (Russian) “Mir,”Moscow, 1970;English original, Wiley, New York, 1964.
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The original manuscript was prepared for publication by D. Paatashvili.
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Chanturia, T. On conjugacy of high-order linear ordinary differential equations. Georgian Mathematical Journal 1, 1–8 (1994). https://doi.org/10.1007/BF02315299
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DOI: https://doi.org/10.1007/BF02315299