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

Clayton da Silva (1) , Alain Jacquemard (2, 3) , Marco Teixeira (4)

1 ICEN - Instituto de Ciências Exatas e Naturais
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]
3 PolSys - Polynomial Systems
4 IMECC - Instituto de Matemática, Estatística e Computação Científica [Brésil]

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.

Mots clés: Second order Periodic solutions; Non-autonomous; Non-autonomous Filippov systems; Filippov systems; Second order; Non-smooth differential equations; Periodic solutions

Domaines: Mathématiques [math]

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⟩