Abel-like differential equations with no periodic solutions

J. L. Bravo; J. Torregrosa

doi:https://doi.org/10.1016/j.jmaa.2007.12.060

Abel-like differential equations with no periodic solutions

J. L. Bravo, J. Torregrosa

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

17 Citations (Scopus)

Abstract

We present various criteria for the non-existence of positive periodic solutions of generalized Abel differential equations with periodic coefficients that can change sign. As an application, we obtain some families of planar vector fields without limit cycles. © 2007 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	931-942
Journal	Journal of Mathematical Analysis and Applications
Volume	342
DOIs	https://doi.org/10.1016/j.jmaa.2007.12.060
Publication status	Published - 15 Jun 2008

Keywords

Abel equation
Hilbert's 16th problem
Limit cycles
Periodic solutions
Rigid systems

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https://doi.org/10.1016/j.jmaa.2007.12.060

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title = "Abel-like differential equations with no periodic solutions",

abstract = "We present various criteria for the non-existence of positive periodic solutions of generalized Abel differential equations with periodic coefficients that can change sign. As an application, we obtain some families of planar vector fields without limit cycles. {\textcopyright} 2007 Elsevier Inc. All rights reserved.",

keywords = "Abel equation, Hilbert's 16th problem, Limit cycles, Periodic solutions, Rigid systems",

author = "Bravo, {J. L.} and J. Torregrosa",

year = "2008",

month = jun,

day = "15",

doi = "https://doi.org/10.1016/j.jmaa.2007.12.060",

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TY - JOUR

T1 - Abel-like differential equations with no periodic solutions

AU - Bravo, J. L.

AU - Torregrosa, J.

PY - 2008/6/15

Y1 - 2008/6/15

N2 - We present various criteria for the non-existence of positive periodic solutions of generalized Abel differential equations with periodic coefficients that can change sign. As an application, we obtain some families of planar vector fields without limit cycles. © 2007 Elsevier Inc. All rights reserved.

AB - We present various criteria for the non-existence of positive periodic solutions of generalized Abel differential equations with periodic coefficients that can change sign. As an application, we obtain some families of planar vector fields without limit cycles. © 2007 Elsevier Inc. All rights reserved.

KW - Abel equation

KW - Hilbert's 16th problem

KW - Limit cycles

KW - Periodic solutions

KW - Rigid systems

U2 - https://doi.org/10.1016/j.jmaa.2007.12.060

DO - https://doi.org/10.1016/j.jmaa.2007.12.060

M3 - Article

SN - 0022-247X

VL - 342

SP - 931

EP - 942

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

ER -

Abel-like differential equations with no periodic solutions

Abstract

Keywords

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