Periodic solutions of Lienard differential equations via averaging theory of order two

Jaume Llibre; Douglas D. Novaes; Marco A. Teixeira

doi:https://doi.org/10.1590/0001-3765201520140129

Periodic solutions of Lienard differential equations via averaging theory of order two

Jaume Llibre, Douglas D. Novaes, Marco A. Teixeira

Department of Mathematics

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

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Abstract

© 2015 Academia Brasileira de Ciencias. All rights reserved. For ε ≠ 0sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form (formula presented) where n is a positive integer, f : ℝ → ℝis a C 3function, g : ℝ → ℝis a C4function, and p i : ℝ → ℝfor i = 1 , 2are continuous 2 π–periodic function. The main tool used in this paper is the averaging theory of second order. We also provide one application of the main result obtained.

Original language	English
Pages (from-to)	1905-1913
Journal	Anais da Academia Brasileira de Ciencias
Volume	87
Issue number	4
DOIs	https://doi.org/10.1590/0001-3765201520140129
Publication status	Published - 1 Oct 2015

Keywords

Averaging theory
Bifurcation theory
Lienard differential equation
Periodic solution

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title = "Periodic solutions of Lienard differential equations via averaging theory of order two",

abstract = "{\textcopyright} 2015 Academia Brasileira de Ciencias. All rights reserved. For ε ≠ 0sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form (formula presented) where n is a positive integer, f : ℝ → ℝis a C 3function, g : ℝ → ℝis a C4function, and p i : ℝ → ℝfor i = 1 , 2are continuous 2 π–periodic function. The main tool used in this paper is the averaging theory of second order. We also provide one application of the main result obtained.",

keywords = "Averaging theory, Bifurcation theory, Lienard differential equation, Periodic solution",

author = "Jaume Llibre and Novaes, {Douglas D.} and Teixeira, {Marco A.}",

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T1 - Periodic solutions of Lienard differential equations via averaging theory of order two

AU - Llibre, Jaume

AU - Novaes, Douglas D.

AU - Teixeira, Marco A.

PY - 2015/10/1

Y1 - 2015/10/1

N2 - © 2015 Academia Brasileira de Ciencias. All rights reserved. For ε ≠ 0sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form (formula presented) where n is a positive integer, f : ℝ → ℝis a C 3function, g : ℝ → ℝis a C4function, and p i : ℝ → ℝfor i = 1 , 2are continuous 2 π–periodic function. The main tool used in this paper is the averaging theory of second order. We also provide one application of the main result obtained.

AB - © 2015 Academia Brasileira de Ciencias. All rights reserved. For ε ≠ 0sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form (formula presented) where n is a positive integer, f : ℝ → ℝis a C 3function, g : ℝ → ℝis a C4function, and p i : ℝ → ℝfor i = 1 , 2are continuous 2 π–periodic function. The main tool used in this paper is the averaging theory of second order. We also provide one application of the main result obtained.

KW - Averaging theory

KW - Bifurcation theory

KW - Lienard differential equation

KW - Periodic solution

U2 - https://doi.org/10.1590/0001-3765201520140129

DO - https://doi.org/10.1590/0001-3765201520140129

M3 - Article

SN - 0001-3765

VL - 87

SP - 1905

EP - 1913

JO - Anais da Academia Brasileira de Ciencias

JF - Anais da Academia Brasileira de Ciencias

IS - 4

ER -

Periodic solutions of Lienard differential equations via averaging theory of order two

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Keywords

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