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

Timoteo Carletti, Lilia Rosati, Gabriele Villari

Research output: Contribution to journalArticle

### Abstract

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 uniqueness of limit cycles are presented. In particular, a generalization of the classical Massera uniqueness result is proved.
Original language English 39-51 13 NonlinearAnalysis 67 Published - 2007

### Keywords

• Qualitative theory
• Planar vector fields
• Limit cycles