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

Timoteo Carletti

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

Research output: Book/Report/Journal › Other report

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
Place of Publication	Namur
Publisher	FUNDP, Faculté des Sciences. Département de Mathématique.
Publication status	Published - 2007

Keywords

Qualitative theory
Planar vector fields
Limit cycles

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",

note = "Publication code : FP SB010/2007/21 ; QA 0002.2/001/07/21",

year = "2007",

language = "English",

publisher = "FUNDP, Facult{\'e} des Sciences. D{\'e}partement de Math{\'e}matique.",

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

AU - Carletti, Timoteo

N1 - Publication code : FP SB010/2007/21 ; QA 0002.2/001/07/21

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 - Other report

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

PB - FUNDP, Faculté des Sciences. Département de Mathématique.

CY - Namur

ER -

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

Abstract

Keywords

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