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

Timoteo Carletti; Lilia Rosati; Gabriele Villari

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 journal › Article › peer-review

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
Pages (from-to)	39-51
Number of pages	13
Journal	NonlinearAnalysis
Volume	67
Publication status	Published - 2007

Keywords

Qualitative theory
Planar vector fields
Limit cycles

Two days on qualitative theory of differential equations
Timoteo Carletti (Speaker)
30 Sept 2022 → 1 Oct 2022
Activity: Participating in or organising an event types › Participation in workshop, seminar, course

Cite this

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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",

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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 -

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

Abstract

Keywords

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Activities

Two days on qualitative theory of differential equations

Cite this