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Abstract
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In this paper, a new structure of an applied model of thermostat is defined using the
generalized \psi-operators with three-point boundary conditions. Some useful properties of the relevant
Green’s function are established, and based on these properties, the Lyapunov-type inequality is
constructed for the given extended \psi-model thermostat with the help of Jensen’s inequality. By
defining mild solutions for such an extended system, the existence and non-existence conditions
are discussed.
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