Abstract
The sets of values (spectra) of the oscillation indices of strict signs, nonstrict signs, zeros,roots, and hyperroots of solutions of differential systems are studied. Two-dimensional nonlinearsystems are constructed all of whose solutions are infinitely extendable to the right and any of thespectra of their oscillation indices can coincide with the interval \([0,1]\) as well as with any prescribed nonempty subset ofrational numbers of this interval, while the spectra of the linear first approximation systemsconsist of only one element. Moreover, the spectra of indices of the original system coincide withthe corresponding spectra of oscillation indices of the restriction of the constructed nonlineartwo-dimensional systems to the direct product of any open neighborhood of zero of the phaseplane by the time half-line. In addition, the existence of a nonlinear system is proved for whichthe spectrum of any of the oscillation indices in question coincides with an arbitrary prescribedsubinterval of \([0,1]\) , while the corresponding spectra of the firstapproximation system consist of one nonnegative number.
