Periodic oscillations in systems with hysteresis

We give precise conditions under which the method of harmonic balance will correctly predict the existence of periodic solutions for a system with relay hysteresis. The equation modeling the system is assumed to be of the form L(m)[y](t) = f[y](t), t greater-than-or-equal-to 0, where L(m) is a constant coefficient linear differential operator of order m greater-than-or-equal-to 2 and f is a possibly discontinuous operator with hysteresis