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

Résultats de recherche: Contribution à un journal/une revue › Article › Revue par des pairs

Résumé

Le portrait de phase de l'équation du deuxième ordre $$ \ddot{x} + \sum_{l=0}^n f_l(x)\dot{x}^l=0, $$ est étudié. Certains résultats sur l'existence, la non-existence et l'unicité de cycles limites sont présentés. Notamment, a généralisation du résultat classique de Massera concernant l'unicité de cycles limites est démontré.

langue originale	Anglais
Pages (de - à)	39-51
Nombre de pages	13
journal	NonlinearAnalysis
Volume	67
Etat de la publication	Publié - 2007

Two days on qualitative theory of differential equations
Timoteo Carletti (Conférencier)
30 sept. 2022 → 1 oct. 2022
Activité: Participation ou organisation d'un événement › Participation à un atelier/workshop, un séminaire, un cours

Contient cette citation

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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

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Two days on qualitative theory of differential equations

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