On the problem of stability of a motion of essentially nonlinear systems
Keywords:estimation of the Lyapunov function, essentially nonlinear system, motion, resistance to large disturbances
This article discusses essentially nonlinear systems. Following the approach of applying the pseudolinear inequalities
developed in a number of works, new estimates for the variation of Lyapunov functions along solutions
of the considered systems of equations are obtained. Based on these estimates, we obtain sufficient conditions
for the equiboundedness of solutions of second-order systems and sufficient conditions for the stability of an
essentially nonlinear system under large initial perturbations. Conditions for the stability of affine systems are
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