ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF CERTAIN SECOND ORDER NON-AUTONOMOUS NONLINEAR ORDINARY DIFFERENTIAL EQUATION

Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems

Certain nonlinear autonomous ordinary differential equations of the second order are reduced to Abel equations of the first kind Ab-1 equations . Based on the results of a previous work, concerning a closed-form solution of a general Ab-1 equation, and introducing an arbitrary function, exact one-parameter families of solutions are derived for the original autonomous equations, for the most of ...

Special Function Solutions of a Class of Certain Non-autonomous Nonlinear Ordinary Differential Equations

We apply a direct linearization technique to a class of certain nonlinear n o n a u t o n o m o u s second-order ordinary differential equations with cubic nonlinearities and obtained special function solutions of them .

On the asymptotic behaviour of solutions of certain non-autonomous differential equations

Asymptotic Behaviour of Oscillatory Solutions of a Fourth-order Nonlinear Differential Equation

Asymptotic behaviour of oscillatory solutions of the fourth-order nonlinear differential equation with quasiderivates y[4] + r(t)f(y) = 0 is studied.

Periodic Solutions of Second Order Non-autonomous Differential Systems

We study the existence of nonnegative solutions for second order nonlinear differential systems with periodic boundary conditions. In this class of problems, where the associated Green’s function may take on negative values, and the nonlinear term is allowed to be singular. Our method is based on the Guo-Krasnosel’skii fixed point theorem of cone expansion and compression type, involving a new ...