On the smoothness of conjugation of circle diffeomorphisms with rigid rotations - Borzdyko, V. I. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
We consider the operator which is a variable hysteron that describes, according to the Krasnosel'skii -Pokrovskii scheme, a nonstationary hysteresis nonlinearity with characteristics varying under external influences. We obtain sufficient conditions under which this operator is defined for inputs from the class of functions H1[t0, T] that satisfy the Lipschitz condition on the interval [t0, T].