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.


34C25 Periodic solutions to ordinary differential equations
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations


Zbl 0348.34007
Full Text: EuDML


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