On properties of derivatives of the basic central dispersion in an oscillatory equation \(y'' = q(t)y\) with an almost periodic coefficient \(q\). (English) Zbl 0584.34026

We consider again the same equation \(y'' = q(t)y\), with \(q\) almost periodic, as in the previous review Zbl 0584.34025. The distribution of zeros of the solution may be described through the basic central dispersion \(\phi\) of this equation. The derivatives of this function also are of interest. The author proves that \(\phi\), \(\phi'\), \(\phi''\) are almost periodic functions.


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


Zbl 0584.34025
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[1] Bartůšek M.: On relations among dispersions of an oscillatory differential equation y” = q(t)y. Acta Univ. Palackianae Olomucensis FRN, 41, 1973, 55 - 61.
[2] Borůvka O.: Linear Differential Transformations of the Second Order. The English Univ. Press, London, 1971. · Zbl 0218.34005
[3] Борувка О.: Тєория глобальных свойств обыкновєнных лунєйных диффєрєнциальных уравнєний второго порядка. Диффєрєнциальныє уравнєния, Но. 8, t. 12, 1976, 1347-1383.
[4] Hartman P.: Ordinary Differential Equations. (In Russian) Moscow, 1970. · Zbl 0214.09101
[5] Xapacaxan B. X.: Почти-периодические решения обыкновенных дифференциальных уравнений. Издательство Наука, Алма-Ата, 1970.
[6] Staněk S.: On the basic central dispersion of the differential equation y” = q(t)y with an almost periodic coefficient q. Acta Univ. Palackianae Olomucensis, FRN vol. 76, mathematica XXII, 1983, 99-105. · Zbl 0567.34029
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