The existence of periodic solutions for the third-order differential equation ̇̈ x+ ω2ẋ = μF(x,ẋ, ẍ) is studied. We give some conditions for this equation in order to reduce it to a second-order nonlinear differential equation. We show that the existence of periodic solutions for the second-order equation implies the existence of periodic solutions for the above equation. Then we use the Hopf bif...

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations, we extend to the third order by differentiating the second order equation. This yields criteria for linearizability of a class of third order semi-linear ordinary differential equations, which is distinct from the classes available in the literature. Some examples are given and...

Sufficient conditions are established for the ultimate boundedness of solutions of certain third-order nonlinear differential equations. Our result improves on Tunc’s [C. Tunc, Boundedness of solutions of a third-order nonlinear differential equation, J. Inequal. Pure and Appl. Math., 6(1) Art. 3,2005,1-6].