We consider the second-order discontinuous differential equation y″ + η sgn(y) = 𝜃y + α sin(βt) where the parameters η, 𝜃, α, and β 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.
Non-smooth differential equations Second order Periodic solutions Non-autonomous Filippov systems
Mathematics Subject Classification (2010)
34C15 34K12 34H05
This is a preview of subscription content, log in to check access.
Kunze M, Küpper T., You J. On the application of KAM theory to discontinuous dynamical systems. J. Differential Equations 1997;139:1–21.MathSciNetCrossRefGoogle Scholar
Jacquemard A, Teixeira MA. Periodic solutions of a class of non-autonomous second order differential equations with discontinuous right-hand side. Phys D 2012;241: 2003–2009.MathSciNetCrossRefGoogle Scholar