Sliding solutions of second-order differential equations with discontinuous right-hand side

Clayton E. L. da Silva (1) , Paulo R. da Silva (1) , Alain Jacquemard (2, 3)

1 UFMT - Universidade Federal de Mato Grosso
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]
3 PolSys - Polynomial Systems

We consider second-order ordinary differential equations with discontinuous right-hand side. We analyze the concept of solution of this kind of equations and determine analytical conditions that are satisfied by typical solutions. Moreover, the existence and uniqueness of solutions and sliding solutions are studied.

Mots clés: Differential equation; Nonsmooth dynamical system; Filippov system; Sliding solution

Domaines: Mathématiques [math]

Clayton E. L. da Silva, Paulo R. da Silva, Alain Jacquemard. Sliding solutions of second-order differential equations with discontinuous right-hand side. Mathematical Methods in the Applied Sciences, 2017, 40 (14), pp.5295 - 5306. ⟨10.1002/mma.4387⟩. ⟨hal-01609363⟩