Periodic Solutions of a Class of Non-autonomous Discontinuous Second-Order Differential Equations - Université de Bourgogne
Article Dans Une Revue Journal of Dynamical and Control Systems Année : 2020

Periodic Solutions of a Class of Non-autonomous Discontinuous Second-Order Differential Equations

Résumé

We consider the second-order discontinuous differential equation y('') + eta sgn(y) = & x1d703;& xdf03;y + alpha sin(beta t) where the parameters eta, & x1d703;& xdf03;, alpha, and beta are real. The main goal is to discuss the existence of periodic solutions. Under explicit conditions, the number of such solutions is given. Furthermore, for each of these periodic solutions, an explicit formula is provided.

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Mathématiques [math]

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https://u-bourgogne.hal.science/hal-02094522

Soumis le : jeudi 27 juin 2019-11:53:39

Dernière modification le : mardi 19 novembre 2024-14:36:03

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Dates et versions

hal-02094522 , version 1 (27-06-2019)

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Clayton da Silva, Alain Jacquemard, Marco Teixeira. Periodic Solutions of a Class of Non-autonomous Discontinuous Second-Order Differential Equations. Journal of Dynamical and Control Systems, 2020, 26, pp.17-44. ⟨10.1007/s10883-018-9426-7⟩. ⟨hal-02094522⟩

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