Criteria for asymptotic stability of fourth-order nonlinear differential equations with quasi-derivatives

摘要

The paper deals with a certain class of nonautonomous ordinary fourth-order nonlinear differential equations of the type L_4y = f(t, L_0y, L_1y, L_2y, L_3y) with quasi-derivatives. A criterion of asymptotic stability in Liapunov sense as well as a criterion of instability in Liapunov sense is derived. The results are illustrated by proper examples.