Oscillation and Wandering of Solutions to a Second Order Differential Equation / Sergeev I.N. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. № 6. P. 21-26 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].
The Lyapunov's oscillation and wandering characteristics of solutions to a second order linear equation are defined, namely, the mean frequency of a solution, of its derivative or their various linear combinations, the mean angular velocity of the vector composed of a solution and its derivative, also wandering indices derived from that velocity. Nearly all of the values introduced for any equation are proved to be the same: just all for the autonomic equation (moreover, they coincide with the absolute values of the imaginary parts of the roots of the characteristic polynomial), but even for the periodic one, generally speaking, not all.
differential equation, zeros of solutions, oscillation and wandering,