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Many periodic solutions for a second order cubic periodic differential equation

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Abstract

The aim of this work is to provide results that assure the existence of many isolated T-periodic solutions for T-periodic second-order differential equations of the form \(x''=a(t)x + b(t)x^2 + c(t)x^3\). We use bifurcation methods, including Malkin functions and results of Fonda, Sabatini and Zanolin. In addition, we give a general result that assures the existence of a T-periodic perturbation of a non-isochronous center with an arbitrary number of T-periodic solutions.

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Correspondence to Adriana Buică.

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Communicated by Adrian Constantin.

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This work was supported by Ministerio de Ciencia, Innovación y Universidades of the Spanish Government by grants MTM2016-77278-P (MINECO/AEI/FEDER, UE) and 2017-SGR-1617 from AGAUR, Generalitat de Catalunya.

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Buică, A., Gasull, A. Many periodic solutions for a second order cubic periodic differential equation. Monatsh Math 193, 555–572 (2020). https://doi.org/10.1007/s00605-020-01433-4

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  • DOI: https://doi.org/10.1007/s00605-020-01433-4

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