Periodic Solutions of a Class of Non-autonomous Discontinuous Second-Order Differential Equations - Archive ouverte HAL Access content directly
Journal Articles Journal of Dynamical and Control Systems Year : 2020

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

Abstract

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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Dates and 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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