On some special conditions of $n$-th order non-oscillatory nonlinear systems

Abstract

Krylov-Bogoliubov-Mitropolskii method has been extended to obtainasymptotic solution of n-th order nonlinear differential systemcharacterized by certain non-oscillatory processes. The dampingforce is considered in such a manner that one of thecharacteristic roots of the linear system becomes small and othersare in integral multiple. The method is illustrated by an example.The solutions for different initial conditions show a goodagreement with those obtained by numerical method.