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Stability, boundedness and asymptotic behaviour of solutions of certain nonlinear differential equations of the third order
(2011) Ademola, T. A.; Arawomo, P. O.
Criteria are established for uniform asymptotic stability, boundedness, uniform ultimate boundedness and asymptotic behaviour of solutions of certain third order nonlinear differential equations with the restoring nonlinear terms depend on t and multiplied by functions of t. By constructing a complete Lyapunov function, Lyapunov second method, the technique of Antoisewicz [8] and the limit point of Yoshizawa [22] are employed to obtain the results. Recent results on third order nonlinear differential equations and the results which have been discussed in [16] are special cases of our results.
Boundedness results for a certain third order nonlinear differential equation
(Elsevier Inc., 2010) Ademola, T. A.; Ogundiran, M. O.; Arawomo, P. O.; Adesina, O. A.
Sufficient conditions for the existence of solutions to boundedness and ultimate boundedness problems associated to a certain third order nonlinear differential equation are given by means of the Lyapunov’s second method. The appropriate Lyapunov function is given explicitly. Our results complement some well known results on the third order differential equations in the literature.