Abstract.
We consider an ordinary differential equation with hysteresis and time delay in the hysteresis term and also a partial differential equation with hysteresis in the boundary conditions. Both are candidates for the description of a type of thermostat. The considered hysteresis relation is relay hysteresis in both models. The existence of a periodic solution to both equations is shown and the relationship between the two models is discussed.
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Received: January 23, 2001; revised: January 24, 2002
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Kopfová, J., Kopf, T. Differential equations, hysteresis, and time delay. Z. angew. Math. Phys. 53, 676–691 (2002). https://doi.org/10.1007/s00033-002-8176-1
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DOI: https://doi.org/10.1007/s00033-002-8176-1