Hysteresis nonstationary nonlinearities

We consider an operator (variable hysteron) used to describe a nonstationary hysteresis nonlinearity (whose characteristics vary under the action of external forces) according to the Krasnosel’skii-Pokrovskii scheme. Sufficient conditions under which the operator is defined for the inputs from the class of functions H ¹t ₀, T] satisfying the Lipschitz condition in the segment t ₀, T] are established. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 3, pp. 295–309, March, 2008.