Qualitative analysis of phase--portrait for a class of planar vector fields via the comparison method

Timoteo Carletti, Lilia Rosati, Gabriele Villari

The phase--portrait of the second order differential equation: $$\ddot{x}+\sum _{l=0}^n{f}_l(x){\dot{x}}^l=0,$$ is studied. Some results concerning existence, non--existence and uniquen…