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2019 Periodic solutions for a singular Liénard equation with indefinite weight
Shiping Lu, Runyu Xue
Topol. Methods Nonlinear Anal. 54(1): 203-218 (2019). DOI: 10.12775/TMNA.2019.037

Abstract

In this paper, the existence of positive periodic solutions is studied for a singular Liénard equation where the weight function has an indefinite sign. Due to the lack of a priori estimates over the set of all possible positive periodic solutions in this equation, a new method is proposed for estimating a priori bounds of positive periodic solutions. By the use of a continuation theorem of the Mawhin coincidence degree, new conditions for existence of positive periodic solutions to the equation are obtained. The main results show that the singularity of coefficient function associated to the friction term at $x=0$ may help the existence of periodic solutions.

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Shiping Lu. Runyu Xue. "Periodic solutions for a singular Liénard equation with indefinite weight." Topol. Methods Nonlinear Anal. 54 (1) 203 - 218, 2019. https://doi.org/10.12775/TMNA.2019.037

Information

Published: 2019
First available in Project Euclid: 16 July 2019

zbMATH: 07131280
MathSciNet: MR4018276
Digital Object Identifier: 10.12775/TMNA.2019.037

Rights: Copyright © 2019 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.54 • No. 1 • 2019
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