Periodic Properties of Solutions of Certain Second Order Nonlinear Differential Equations

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.