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On the basic central dispersion of the differential equation \(y''=q(t)y\) with an almost periodic coefficient. (English) Zbl 0567.34029
We investigate differential equations of type (q) \(y''=q(t)y\), \(q\in C^ 0({\mathbb{R}})\). The distribution of zeros of solutions of (q) may be described by means of the basic central dispersion \(\phi\) of (q). O. Borůvka proved [Differ. Uravn. 12, 1347-1383 (1976; Zbl 0348.34007)] that the function \(\phi(t)-t\) is \(\pi\)-periodic if the coefficient q of the oscillatory equation (q) also is \(\pi\)-periodic.

MSC:
34C25 Periodic solutions to ordinary differential equations
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
Citations:
Zbl 0348.34007
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References:
[1] Borůvka O.: Linear Differential Transformations of the Second Order. The English Universities Press, London, 1971. · Zbl 0218.34005
[2] Борувка О.: Тєоруя глобалъных свойсмв обыкновєнных лунєйных дуффєрєнцуалъных уравнєнуй вморого порядка. Диффєрєнциальныє уравнєния По 8, t. XII, 1976, 1347-1383.
[3] Hartman P.: Ordinary Differential Equations. (In Russian) Moscow, 1970. · Zbl 0214.09101
[4] Xapacaxan B. X.: Почму-пєруодучєскує рєчєнуя lобыкновєнных дуффєрєнцуальных уравнєнуй. Издатєльство ”Наука”, Алма-Ата, 1970.
[5] 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
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