Gouveia, Márcio R.A. [UNESP]Llibre, JaumeNovaes, Douglas D.Pessoa, Claudio [UNESP]2018-12-112018-12-112016-04-05Journal of Differential Equations, v. 260, n. 7, p. 6108-6129, 2016.1090-27320022-0396http://hdl.handle.net/11449/172533We consider an n-dimensional piecewise smooth vector field with two zones separated by a hyperplane σ which admits an invariant hyperplane Ω transversal to σ containing a period annulus A fulfilled by crossing periodic solutions. For small discontinuous perturbations of these systems we develop a Melnikov-like function to control the persistence of periodic solutions contained in A. When n=3 we provide normal forms for the piecewise linear case. Finally we apply the Melnikov-like function to study discontinuous perturbations of the given normal forms.6108-6129engCrossing periodic solutionsLimit cyclesLyapunov-Schmidt reductionNormal formsPiecewise differential systemArtigo10.1016/j.jde.2015.12.034Acesso restrito2-s2.0-8495812002437249378865574240000-0001-6790-1055