zbMATH — the first resource for mathematics

On the basic second kind central dispersion of \(y''=q(t)y\) with an almost periodic coefficient q. (English) Zbl 0584.34025
Let \(y''=q(t)y\), \(C\in C^ 0(R)\), \(q(t)<0\) for \(t\in R\), be an oscillatory equation with an almost periodic coefficient q. The distribution of zeros of the derivative of solutions of this equation is described by \(\psi\), the basic second kind central dispersion of this equation. The author proves that the function \(t\to \psi (t)-t\) is almost periodic.
Reviewer: J.E.Rubio

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
Full Text: EuDML
[1] Borůvka O.: Linear Dìfferential Transformations of the Second Order. T\?e English Univ. Press, London, 1971. · Zbl 0222.34002
[2] Борувка О.: Тєория глобальных свойств обыкновєнных лунєйных диффєрєнциальных уравнєний второго порядка. Диффєрєнциальныє уравнєния, Но. 8, t. 12, 1976, 1347-1383.
[3] Xapacaxan B. X.: Почму-пєруодичєскує рєшєния обыкновєнных диффєрєнциальных уравнєний. Издатєльство ”Наука”, Алма-Ата, 1970.
[4] Markus L., Moore R. A.: Oscillation and disconjugacy for linear differential equations with almost periodic coefficients. Acta Math., 96, 1956, 99 - 123. · Zbl 0071.08302
[5] 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, F. R. N., vol. 76, mathematica XXII, 1983, 99-105. · Zbl 0567.34029
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.