Alexey A. Bondarev

An Example of Contrasting Combination to Stability and Instability Properties in Even-Dimensional Spaces

abstract:
It was constructed examples of even-dimensional differential systems having, in a some sense, contrary stability and instability properties of different types: Lyapunov, Perron and upper-limit. Namely, all nonzero solutions of these systems tend to zero at infinity but nevertheless move away at the fixed distance from the origin at least once. In addition, these systems have a zero first approximation along the zero solution.

Mathematics Subject Classification: 34D05, 34D20, 34D23

Key words and phrases: Differential equations, nonlinear systems, Lyapunov stability, Perron stability, upper-limit stability