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...

In this paper, the following third-order nonlinear delay differential equation with periodic coefficients x′′′(t) + p(t)x′′(t) + q(t)x′(t) + r(t)x(t) = f (t, x (t) , x(t− τ(t))) + c(t)x′(t− τ(t)), is considered. By employing Green’s function and Krasnoselskii’s fixed point theorem, we state and prove the existence of positive periodic solutions to the third-order delay differential equation.

We study symmetry and holomorphy of the third-order ordinary differential equation satisfied by the third Painlevé Hamiltonian.

We study symmetry and holomorphy of the third-order ordinary differential equation defined by the third Painlevé Hamiltonian.

For third order linear differential equations of the form r(t)x'(t)''+ p(t)x'(t) + q(t)x(t) = 0; we will establish lower bounds for distance between zeros a solution and/or its derivatives. The main results be proved by making use Hardyís inequality, some generalizations Opialís inequality and Boydís inequality.