# 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

### Fingerprint

Planar Vector Fields
Comparison Method
Phase Portrait
Nonuniqueness
Qualitative Analysis
Second order differential equation
Limit Cycle
Nonexistence
Existence Results
Uniqueness
Generalization
Class

### Keywords

• Qualitative theory
• Planar vector fields
• Limit cycles

### Cite this

title = "Qualitative analysis of the phase portrait for a class of planar vector fields via the comparison method",
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.",
keywords = "Qualitative theory, Planar vector fields, Limit cycles",
author = "Timoteo Carletti and Lilia Rosati and Gabriele Villari",
year = "2007",
language = "English",
volume = "67",
pages = "39--51",
journal = "NonlinearAnalysis",

}

Qualitative analysis of the phase portrait for a class of planar vector fields via the comparison method. / Carletti, Timoteo; Rosati, Lilia; Villari, Gabriele.

In: NonlinearAnalysis, Vol. 67, 2007, p. 39-51.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Qualitative analysis of the phase portrait for a class of planar vector fields via the comparison method

AU - Carletti, Timoteo

AU - Rosati, Lilia

AU - Villari, Gabriele

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - Qualitative theory

KW - Planar vector fields

KW - Limit cycles

M3 - Article

VL - 67

SP - 39

EP - 51

JO - NonlinearAnalysis

JF - NonlinearAnalysis

ER -