By using the method of functional analysis, especially \(C_0\)-semigroup theory and spectral theory of linear operators we prove the well-posedness and the existence of a unique positive dynamic solution of a deteriorating system with multiple vacations of a repairman. Moreover, we show spectral properties of the system operator which imply that the system does not have a steady-state solution.

中文翻译：

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修理工多次休假的恶化系统的半群方法

通过使用泛函分析的方法，尤其是\（C_0 \）-半群理论和线性算子的谱理论，我们证明了随着修理工多次休假而恶化的系统的适定性和存在的唯一正动力解的存在。此外，我们显示了系统算子的频谱特性，这表明系统没有稳态解。