Periodic Solutions of Continuous Third-Order Differential Equations with Piecewise Polynomial Nonlinearities

J. Llibre; B. D. Lopes; J. R. De Moraes

doi:10.1142/S0218127420501588

Periodic Solutions of Continuous Third-Order Differential Equations with Piecewise Polynomial Nonlinearities

J. Llibre^*, B. D. Lopes, J. R. De Moraes

^*Corresponding author for this work

Department of Mathematics

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

2 Citations (Scopus)

Abstract

We consider third-order autonomous continuous piecewise differential equations in the variable x. For such differential equations with nonlinearities of the form xm, we investigate their periodic solutions using the averaging theory. We remark that since the differential system is only continuous we cannot apply to it the classical averaging theory, that needs that the differential system be at least of class C2.

Original language	English
Article number	2050158
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	30
Issue number	11
DOIs	https://doi.org/10.1142/S0218127420501588
Publication status	Published - 15 Sept 2020

Keywords

Periodic solution
averaging method
piecewise differential equation
third-order differential equation

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10.1142/S0218127420501588

https://ddd.uab.cat/record/236654

Cite this

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title = "Periodic Solutions of Continuous Third-Order Differential Equations with Piecewise Polynomial Nonlinearities",

abstract = "We consider third-order autonomous continuous piecewise differential equations in the variable x. For such differential equations with nonlinearities of the form xm, we investigate their periodic solutions using the averaging theory. We remark that since the differential system is only continuous we cannot apply to it the classical averaging theory, that needs that the differential system be at least of class C2.",

keywords = "Periodic solution, averaging method, piecewise differential equation, third-order differential equation",

author = "J. Llibre and Lopes, \{B. D.\} and \{De Moraes\}, \{J. R.\}",

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AU - Llibre, J.

AU - Lopes, B. D.

AU - De Moraes, J. R.

PY - 2020/9/15

Y1 - 2020/9/15

N2 - We consider third-order autonomous continuous piecewise differential equations in the variable x. For such differential equations with nonlinearities of the form xm, we investigate their periodic solutions using the averaging theory. We remark that since the differential system is only continuous we cannot apply to it the classical averaging theory, that needs that the differential system be at least of class C2.

AB - We consider third-order autonomous continuous piecewise differential equations in the variable x. For such differential equations with nonlinearities of the form xm, we investigate their periodic solutions using the averaging theory. We remark that since the differential system is only continuous we cannot apply to it the classical averaging theory, that needs that the differential system be at least of class C2.

KW - Periodic solution

KW - averaging method

KW - piecewise differential equation

KW - third-order differential equation

UR - https://www.scopus.com/pages/publications/85092068860

U2 - 10.1142/S0218127420501588

DO - 10.1142/S0218127420501588

M3 - Article

AN - SCOPUS:85092068860

SN - 0218-1274

VL - 30

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

IS - 11

M1 - 2050158

ER -

Periodic Solutions of Continuous Third-Order Differential Equations with Piecewise Polynomial Nonlinearities

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