Existence and asymptotic stability of the periodic solutions of the Lipschitz system x' (t) = εF(t, x, ε) is hereby studied via the averaging method. The traditional C1 dependence of F(s,·,ε) on z is relaxed to the mere strict differentiability of F(s,·,0) at z = z0 for ε = 0, giving room to potential applications for structured nonsmooth systems. © 2007 American Mathematical Society.
|Journal||Proceedings of the American Mathematical Society|
|Publication status||Published - 1 Oct 2007|
- Averaging method
- Fixed point
- Nonsmooth Lipschitz system
- Periodic solution
- Poincaré-andronov mapping