On the problem of stability of a motion of essentially nonlinear systems - Martynyuk, A.A.; Chernienko, V.O. (Reports of the National Academy of Sciences of Ukraine, 2021)
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 also obtained.