In this paper, by defining an appropriate Lyapunov functional, we obtain sufficient conditions for which all solutions of certain real non-autonomous third order nonlinear differential equations are asymptotically stable and bounded. The results obtained improve and extend some known results in the literature.

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Convergence behaviors of solutions arising from certain system of third-order nonlinear differential equations are studied. Such convergence of solutions corresponding to extreme stability of solutions when P 0 ≠ relates a pair of solutions of the system considered. Using suitable Lyapunov functionals, we prove that the solutions of the nonlinear differential equation are convergent. Result obtained generalizes and improves some known results in the literature. Example is included to illustrate the result.

In this paper, we study certain non-autonomous third order delay differential equations with continuous deviating argument and established sufficient conditions for the stability and boundedness of solutions of the equations. The conditions stated complement previously known results. Example is also given to illustrate the correctness and significance of the result obtained.

Periodic properties of solutions play an important role in characterizing the behavior of solutions of sufficiently complicated nonlinear differential equations. Sufficient conditions are established which ensure the existence of periodic (or almost periodic) solutions of certain second nonlinear differential equations. Using the basic tool Lyapunov function, new result on the subject which improve some well known results in the literature with the particular cases of (1) for the existence of almost periodic or periodic solutions when the forcing term $p$ is almost periodic or periodic in t uniformly in $x$ and $\dot{x}$ are obtained. Our result further extends and improves on those that exist in the literature to the more general case considered.