Periodic solutions of discontinuous second order differential systems

Jaume Llibre and Marco Antonio Teixeira

Journal of Singularities
volume 10 (2014), 183-190

Received 2 February 2013. Received in revised form 16 July 2013.

DOI: 10.5427/jsing.2014.10l

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We provide sufficient conditions for the existence of periodic solutions of some classes of autonomous and non-autonomous second order differential equations with discontinuous right-hand sides. In the plane the discontinuities considered are given by the straight lines either x=0, or xy=0. Two applications of these results are made, one to control systems with variable structure, and the other to small external periodic excitation of a discontinuous nonlinear oscillator.


periodic solution, autonomous discontinuous second order differential equations, non-autonomous discontinuous second order differential equations

Mathematical Subject Classification:

34C29, 34C25, 47H11

Author(s) information:

Jaume Llibre Marco Antonio Teixeira
Departament de Matemàtiques Departamento de Matemática
Universitat Autònoma de Barcelona Universidade Estadual de Campinas
08193 Bellaterra Caixa Postal 6065
Barcelona, Catalonia, Spain 13083-970, Campinas, SP, Brazil
email: email: