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 languageEnglish
Pages (from-to)39-51
Number of pages13
JournalNonlinearAnalysis
Volume67
Publication statusPublished - 2007

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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

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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.",
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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

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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

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JO - NonlinearAnalysis

JF - NonlinearAnalysis

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