Asymptotic behavior of solutions of nonlinear systems with multiple imaginary eigenvalues

Abstract

The paper is devoted to the analysis of the decay rate of solutions of a nonlinear system with two pairs of purely imaginary eigenvalues. The main result is the power estimate for the norm of solutions. It is proven that the order of such estimate varies for cases of a diagonalizable matrix of linear approximation, and for a matrix containing a Jordan block. Another result of this work provides sufficient asymptotic stability conditions regardless of forms higher than the third order.