Generalization of some qualitative behaviour of Solutions of third order nonlinear differential equations

Abstract

Criteria for uniform asymptotic stability, boundedness, uniform ultimate boundedness and asymptotic behaviour of solutions of the most general third order nonlinear differential equations with the restoring nonlinear terms depending explicitly on the independent real variable t are established. The construction a complete Lyapunov function, Lyapunov’s second method, the technique introduced by Antoisewicz [9] and the limit point of Yoshizawa [29] are used to obtain the results. The most recent results of Ademola and Arawomo [1, 2, 3, 4] and results on third order nonlinear differential equations which have been discussed in [18] are particular cases of our results.