Abstract:
Examples of two linear homogeneous differential equations of the third order are constructed, the spectra of the upper strong exponents of oscillation of signs, zeros and roots of one of which coincide with the set of rational numbers of the segment $[0,1]$, and the other with the set of irrational numbers of the segment $[0,1]$ augmented with the number zero.
Key words:differential equations, oscillation, number of zeros, exponents of oscillation, Sergeev frequencies, Lyapunov exponents.