Composed perturbations to a coupled ODEs system with hysteresis

In this paper, we address a system of two ODEs including a hysteresis nonlinearity of generalized play type. Our system is subject to a composed perturbation, giving under particular choices of composants various types of common multivalued perturbations. We prove the existence of a solution to this system. The theoretical analysis is complemented by a discussion of a mechanical model illustrating potential applicability of our results and the physical meaning of the underlying assumptions.